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The Belousov-Zhabotinsky reaction reveals two regimes of non-Arrhenius temperature scaling in relaxation oscillators

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that non-Arrhenius temperature scaling in relaxation oscillators has two distinct mechanistic origins—Arrhenius-dependent timescale separation producing biphasic scaling, and Arrhenius-dependent nullclines hiding a Hopf…

desk verdict A useful two-regime framework and a great BZ dataset, but the classical-reaction quantitative chain is built on an R_epsilon ∝ epsilon identification that contradicts the model's own constant-epsilon assumption. read the letter →

arxiv 2608.06979 v1 pith:IRKKUOGW submitted 2026-08-07 nlin.CD

Simen Jacobs , Nikita Frolov , Panna Farkas , István Lagzi , István Szalai , Lendert Gelens This is my paper · ORCID
classification nlin.CD MSC 34E1537G1537N25
keywords temperaturescalingArrheniuslawnon-ArrheniusbehaviorrelaxationoscillatorBelousov-ZhabotinskyreactionHopfbifurcationcanardexplosiontimescaleseparation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that non-Arrhenius temperature scaling in relaxation oscillators is not a collection of circuit-specific accidents but follows from the fast-slow structure shared by all such oscillators. Using the Belousov-Zhabotinsky (BZ) reaction over roughly 100 degrees Celsius, it identifies two regimes: one where temperature changes the timescale separation between fast and slow variables, producing a curved, biphasic Arrhenius plot as the system approaches a supercritical Hopf bifurcation; another where temperature shifts the nullclines and a canard explosion hides the same bifurcation, so the period looks like a single Arrhenius line. The paper shows the classical catalyzed BZ reaction occupies the second regime and the uncatalyzed variant the first, and that the measured falling-to-rising phase ratio of the waveform quantitatively predicts the period, amplitude, and phase noise near the bifurcation. If correct, this provides a general, waveform-based diagnostic for how close any biochemical relaxation oscillator is to losing its oscillations.

What carries the argument

The load-bearing objects are the timescale-separation parameter epsilon and the waveform asymmetry ratio R_epsilon. In the generic two-variable relaxation oscillator, epsilon separates fast and slow phases, and the period has a relaxation-oscillator limit independent of epsilon plus a Hopf limit proportional to a power of epsilon. The canard explosion is the mechanism that compresses the Hopf limit into an unobservably narrow temperature window when only the nullclines move with temperature. R_epsilon, the ratio of falling to rising phase durations, is the experimental handle: it equals 1 for a sinusoid, scales with epsilon in the models, and its Arrhenius slope gives E_epsilon, which then quantitatively predicts the period slope, amplitude decay, and phase-noise growth near the Hopf bifurcation.

What would settle it

Measure R_epsilon and the period simultaneously through an independently characterized supercritical Hopf bifurcation in a relaxation oscillator—for example, a BZ variant whose Hopf locus is known from stoichiometry rather than inferred—and check whether the period's high-temperature activation energy shifts by exactly E_epsilon extracted from R_epsilon; if the shift differs or R_epsilon becomes decorrelated from the timescale separation, the central prediction fails.

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Extended reading notes

Core claim

The central discovery is that a relaxation oscillator's temperature response is controlled by which parameter carries the Arrhenius dependence. If the timescale separation parameter epsilon itself obeys an Arrhenius law, the period shows two straight-line regimes in an Arrhenius diagram—the relaxation-oscillator limit with slope E_t and the Hopf limit with slope E_t + E_epsilon/2—joined by a smooth crossover. If instead only the nullclines move with temperature while epsilon stays small, the Hopf bifurcation sits inside a canard explosion so narrow that the period follows a single Arrhenius line all the way to the bifurcation. The waveform asymmetry, defined as the ratio R_epsilon of falling to rising phase durations (R_epsilon = 1 for a sine wave and proportional to epsilon in the models), carries the timescale-separation information. Measuring R_epsilon in two BZ reactions over a wide temperature range yields E_epsilon = -29 kJ/mol for the classical reaction and -34 kJ/mol for the uncatalyzed reaction, and these values predict, without additional fitting, the high-temperature slope of the period, the amplitude collapse, and the growth of period variance near the Hopf bifurcation. The classical BZ reaction stays in the canard- and relaxation-oscillator regime, while the uncatalyzed reaction crosses into the Hopf regime.

Load-bearing premise

The argument stands on the assumption that the electrode-potential waveform's falling-to-rising phase ratio R_epsilon is proportional to the model's timescale-separation parameter epsilon across the entire roughly 100-degree temperature range; if that proportionality drifts, the extracted activation energies and all derived predictions lose their quantitative anchor.

Editorial extensions

If this is right

  • If the central claim is correct, the classical catalyzed BZ reaction should show a single Arrhenius period over any experimentally accessible range, with the Hopf bifurcation hidden by a canard explosion and E_t corresponding to the Ce4+ consumption step.
  • The uncatalyzed BZ reaction should show a biphasic Arrhenius period, with the high-temperature slope shifted by E_epsilon, an amplitude that collapses near the Hopf bifurcation, and period variance that grows nonlinearly there.
  • The waveform asymmetry R_epsilon is a quantitative proxy for the timescale separation, so its slope gives E_epsilon without fitting the period, amplitude, or noise data.
  • Near a Hopf bifurcation, temperature compensation in biological clocks generically fails even if E_t is near zero, because the period then scales with E_epsilon rather than E_t, and the phase noise grows nonlinearly.
  • The reduced two-variable models with only a few Arrhenius parameters can capture many independent observables because timescale separation suppresses network details and Arrhenius rates dominate polynomial temperature dependencies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same R_epsilon diagnostic could be applied to biological oscillators: an oscillator whose waveform asymmetry rises with temperature would be flagged as approaching a Hopf bifurcation even if its period still looks Arrhenius.
  • This suggests that recording waveform shape, not just period, in temperature-response studies could reveal hidden bifurcations in systems where the period alone appears linear.
  • The identification of E_epsilon with the autocatalytic HBrO2 step could be tested directly by measuring that elementary activation energy in isolation, outside the oscillatory context.
  • A system engineered to sit near the Hopf boundary at two different temperatures but with the same R_epsilon would allow a clean test of whether phase-noise scaling tracks waveform asymmetry rather than the chemical details of the oscillator.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript develops a two-regime theory for temperature scaling of relaxation oscillators: (i) Arrhenius-dependent timescale separation ε produces biphasic Arrhenius period scaling as the oscillator approaches a supercritical Hopf bifurcation, and (ii) Arrhenius-dependent nullclines with constant ε hide the Hopf bifurcation behind a canard explosion, yielding apparent single-Arrhenius scaling. The authors apply this framework to the classical and uncatalyzed Belousov-Zhabotinsky reactions, using the measured falling-to-rising phase ratio R_ε as a proxy for ε. They report that the uncatalyzed reaction exhibits biphasic period scaling, amplitude decay, and enhanced phase noise near the Hopf bifurcation, while the classical reaction remains in the relaxation-oscillator limit with apparent Arrhenius scaling. They further claim that R_ε quantitatively predicts the temperature scaling of the period, amplitude, and phase noise, and they extract activation energies including a new estimate for the autocatalytic HBrO2 step.

Significance. If the framework can be made internally consistent, the paper would be valuable: it provides explicit asymptotic formulas for the relaxation-oscillator and Hopf limits, a cross-observable validation strategy that uses waveform asymmetry as an independent input for the uncatalyzed period prediction, and a very wide temperature dataset with public code and data. The two-regime distinction — biphasic versus canard-hidden Hopf — is a clear and testable organizing principle for non-Arrhenius scaling in relaxation oscillators. However, the quantitative single-parameter claim is currently demonstrated convincingly only for the uncatalyzed reaction. For the classical BZ reaction the identification of the R_ε slope with E_ε conflicts with the model assumption that ε is constant, and the amplitude prediction requires a fitted constant C. These issues must be resolved before the paper's central claim is fully supported.

major comments (3)
  1. [Sec. III, Eq. (9); Sec. IV, Prediction 1; Sec. V] The classical-BZ model is explicitly built on the assumption that ε is temperature-independent ('we therefore take ε constant'), with all temperature dependence placed in q. Prediction 1 then fits the classical R_ε to an Arrhenius law and names the slope E_ε = −29 kJ/mol, and Section V uses this value to extract a 22 kJ/mol autocatalytic activation energy. Because the text states R_ε ∝ ε in the ODE models (Supplemental Material, Section VIII A), a constant ε would predict a constant R_ε, contradicting Fig. 4A. If instead R_ε varies because q shifts the nullcline or because the electrode potential is a nonlinear transform of the model variable v, then the Arrhenius slope of R_ε cannot be assigned to E_ε. This contradiction is load-bearing for the classification of the classical reaction as Case 2 and for the autocatalytic-energy estimate. Please either revise the classical model to allow ε(T) and re-derive the canard classification, or clearly redefine what E_ε means for the classical reaction and remove the affected quantitative claims.
  2. [Sec. III, paragraph after Eq. (9)] The supercriticality of the Hopf bifurcation in the classical model is asserted by fixing f = 1, justified only by the statement that subcritical bifurcations require f < 1, outside the 'experimentally relevant range' f ∈ (1,2). The stoichiometric parameter f is not measured in the experiments, and the scaling of period, amplitude, and phase noise near a subcritical Hopf bifurcation differs from the supercritical behavior assumed elsewhere in the paper. Please provide experimental or mechanistic support for f = 1, or test how sensitive the two-regime classification and the predicted scalings are to f near 1.
  3. [Sec. IV, Prediction 3, Eq. (17)] The amplitude prediction is not parameter-free: C is fitted to the high-temperature data, and the authors report only qualitative agreement at intermediate temperatures. The abstract's claim that a single parameter quantitatively predicts the amplitude is therefore overstated. Please report the fitted value of C, quantify the agreement (e.g., residuals or confidence intervals), and qualify the amplitude claim appropriately.
minor comments (4)
  1. [Fig. 1B and Sec. I] The text states a temperature range of approximately 100°C, but this appears to apply mainly to the uncatalyzed variant; please state the temperature range for each reaction explicitly in the caption or main text.
  2. [Sec. IV, Prediction 2] The high-temperature period line for the uncatalyzed reaction should include the propagated uncertainty from E_ε (obtained from R_ε) and E_t; as plotted, the line appears deterministic and gives no indication of the uncertainty in the prediction.
  3. [Sec. IV, Prediction 4] No asymptotic prediction is given for σ_P near the Hopf bifurcation, so the upward curvature in Fig. 4D' is only compared qualitatively; adding the predicted scaling would strengthen the claim that phase noise is a quantitative diagnostic.
  4. [Sec. V, first paragraph] The claim of 'eight independent temperature-dependent observables (four per reaction)' overcounts the independent tests, since R_ε is the input observable and the amplitude prediction uses an additional fitted C; please revise the counting and the independence claim.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the waveform-based period prediction is a genuine cross-observable test; only minor non-load-bearing self-citation and an internal-consistency caveat in the classical E_epsilon assignment.

full rationale

The central derivation chain is not circular. Section II derives, from the fast-slow structure of Eq. (2), the RO-limit period (3), the Hopf-limit period (4), and the two temperature-scaling scenarios (Arrhenius-dependent epsilon versus Arrhenius-dependent nullclines) from those limits. The reduced BZ models in Section III are anchored to external sources (Tyson-Fife [32] for the classical Oregonator, Szalai et al. [33] for the uncatalyzed skeleton model), with the parameter-temperature mappings stated to be derived in the Supplement. The key experimental test, Prediction 2 for the uncatalyzed reaction, uses E_epsilon obtained from the independently defined waveform ratio R_epsilon to set the high-temperature period slope E_t+E_epsilon without refitting the period, so it is a genuine cross-observable prediction rather than a fit to the predicted quantity. The amplitude prediction (17) does fit one prefactor C to high-temperature data, but the slope is fixed by E_epsilon; this is disclosed and does not reduce the central claim to its inputs. Self-citations such as refs [12] and [28] appear in supporting discussion and are not load-bearing for the quantitative derivation. I find no step where an output equals an input by construction. One caveat, which is a correctness risk rather than circularity: Section III takes epsilon constant in the classical model (Eq. 9), whereas Prediction 1 fits the classical R_epsilon to an Arrhenius slope and names it E_epsilon under the relation R_epsilon ∝ epsilon; the paper should reconcile this inconsistency, but it does not make the uncatalyzed-reaction validation circular.

Assumptions & free parameters 7 free parameters · 7 assumptions · 0 invented entities

The central predictive quantities are activation energies extracted from fits (E_epsilon, E_t, amplitude conversion factor, and the constant C), plus standard model parameters taken from the BZ literature. The framework rests on standard asymptotic and QSSA assumptions, with the key domain assumption being R_epsilon proportional to epsilon.

free parameters (7)
  • E_epsilon (classical BZ) = -29 kJ/mol
    Arrhenius slope of waveform asymmetry R_epsilon; used to predict high-temperature period and amplitude scaling.
  • E_epsilon (uncatalyzed BZ) = -34 kJ/mol
    Arrhenius slope of R_epsilon; approaches sinusoid at high temperatures.
  • E_t (classical BZ) = 68.8 +/- 0.2 kJ/mol
    Arrhenius slope of period in the RO limit; attributed to bromomalonic acid oxidation step.
  • E_t (uncatalyzed BZ) = 75.1 +/- 0.3 kJ/mol
    Low-temperature Arrhenius slope of period; high-temperature slope predicted as E_t + E_epsilon.
  • Amplitude calibration factor = fitted at low temperatures
    Converts electrode-potential amplitudes to model amplitudes Delta v; fitted where Delta v is assumed constant.
  • C in amplitude prediction (Eq. 17) = fitted to high-temperature amplitude data
    Only free parameter in Delta v/Delta v0 = 1 - C exp(2 E_epsilon/(3RT)); makes the amplitude prediction partly a fit.
  • q0 and epsilon0 (room-temperature model parameters) = q0 = 8e-4, epsilon0 = 7.5e-4
    Typical literature values used for simulations, not for experimental scaling predictions.
assumptions (7)
  • domain assumption Model parameters follow Arrhenius temperature dependence with constant activation energies (epsilon, q, t/tau).
    Used throughout Sections II-IV to translate parameter changes into period scaling; motivated by product-of-rate-constants reduction but not independently verified for each parameter.
  • domain assumption R_epsilon is proportional to epsilon in the ODE models.
    Basis for converting measured waveform asymmetry into epsilon and E_epsilon; referenced to Supplemental Section VIII A.
  • domain assumption Br- and fast variables are eliminated by quasi-steady-state approximation in both BZ models.
    Standard BZ reduction (Tyson-Fife, Szalai et al.), adopted without re-derivation; all conclusions about nullclines and Hopf bifurcations depend on it.
  • domain assumption Oscillation loss occurs via a supercritical Hopf bifurcation; the classical model is fixed at f=1.
    Section III states subcritical case requires f<1, outside experimental range f in (1,2); this fixes the qualitative scenario.
  • domain assumption Temperature dependence of f is negligible (uncatalyzed) and epsilon's temperature dependence is negligible compared to q (classical).
    Stated in Sections III and IV; later R_epsilon measurements show epsilon itself has a nonzero Arrhenius slope, so this assumption is approximate.
  • domain assumption Phase noise is modeled by a 1D Markov jump process approximation of the ODEs, predicting sigma_P ~ <P>.
    Supplemental Section VI; the experimental test verifies the slope n=1 but not the full noise mechanism.
  • standard math Period asymptotics P_ro + O(epsilon) and P_h = A sqrt(epsilon) in relaxation oscillators.
    Standard multiple-timescale and Hopf normal form results; used to derive the biphasic scaling.

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Cite this review

Pith. "Pith review of The Belousov-Zhabotinsky reaction reveals two regimes of non-Arrhenius temperature scaling in relaxation oscillators." pith.science (2026). https://pith.science/paper/IRKKUOGW

@misc{pith2026260806979,
  author       = {Pith},
  title        = {Pith review of: The Belousov-Zhabotinsky reaction reveals two regimes of non-Arrhenius temperature scaling in relaxation oscillators},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IRKKUOGW}},
  note         = {Machine review of arXiv:2608.06979}
}
read the original abstract

The period of biological and chemical oscillators scales with temperature in a characteristic way. Some oscillators are very well described by an Arrhenius law, while others show systematic deviations. Several frameworks have been proposed to explain such deviations, but they are either phenomenological, focus on activation energy imbalances in specific circuits, or restrict themselves to sequential processes. Here we develop a mechanistic account of the temperature scaling of relaxation oscillators, using the Belousov-Zhabotinsky (BZ) reaction as a model system. We distinguish two typical scenarios by their temperature-scaling signatures. In the first, an Arrhenius-dependent timescale separation parameter produces a biphasic Arrhenius scaling of the period as the oscillator approaches a Hopf bifurcation. In the second, Arrhenius-dependent nullclines hide the same bifurcation behind a canard explosion, yielding apparent single-line Arrhenius scaling. Measuring the electrode potential of a classical and an uncatalyzed BZ reaction, over a very wide temperature range ({\approx} 100 {\deg}C), and comparing to dynamical models, we find that the two reactions represent these two distinct scenarios. Furthermore, we show that a single parameter characterizing the waveform asymmetry between fast and slow phases quantitatively predicts the temperature scaling of three other observables close to the Hopf bifurcation: the period, amplitude, and phase noise. This analysis also recovers elementary activation energies of the BZ mechanism, including a new estimate for the autocatalytic step. We discuss how this framework and its waveform-based diagnostics apply to the analysis of general biochemical relaxation oscillators

Figures

Figures reproduced from arXiv: 2608.06979 by the authors.

Figure 1
Figure 1. B shows the measured periods of the classical and uncatalyzed BZ reactions in such an Arrhenius di￾agram. While the classical reaction is well approxi￾mated by a single Arrhenius line, the uncatalyzed reac￾tion displays a clear convex curvature. Our analysis will show that this difference is not an artifact of the mea￾surement range, but reflects a fundamental difference in how the internal timescales of the two rea… view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Works this paper leans on

50 extracted references · 49 canonical work pages

  1. [1]

    A. Dell, S. Pawar, and V. Savage, Systematic variation in the temperature dependence of physiological and ecolog- ical traits, Proceedings of the National Academy of Sci- ences of the United States of America108, 10591 (2011)

    work page 2011

  2. [2]

    J. H. Brown, J. F. Gillooly, A. P. Allen, V. M. Savage, and G. B. West, Toward a metabolic theory of ecology, Ecology85, 1771 (2004)

    work page 2004

  3. [3]

    Kontopoulos, A

    D.-G. Kontopoulos, A. Sentis, M. Daufresne, N. Glaz- man, A. I. Dell, and S. Pawar, No universal mathemat- ical model for thermal performance curves across traits and taxonomic groups, Nature Communications15, 8855 (2024)

    work page 2024

  4. [4]

    Arnoldi, A

    J.-F. Arnoldi, A. L. Jackson, I. Peralta-Maraver, and N. L. Payne, A universal thermal performance curve arises in biology and ecology, Proceedings of the National Academy of Sciences122, e2513099122 (2025)

    work page 2025

  5. [5]

    Jacobs, J

    S. Jacobs, J. B. Voits, N. Frolov, U. S. Schwarz, and L. Gelens, Understanding the temperature response of biological systems: Part I–phenomenological descriptions and microscopic models, Current Opinion in Systems Bi- ology44, 100577 (2026)

    work page 2026

  6. [6]

    Jacobs, J

    S. Jacobs, J. B. Voits, N. Frolov, U. S. Schwarz, and L. Gelens, Understanding the temperature response of biological systems: Part II—network-level mechanisms and emergent dynamics, Current Opinion in Systems Bi- ology44, 100578 (2026)

    work page 2026

  7. [7]

    C. S. Pittendrigh, On temperature independence in the clock system controlling emergence time in drosophila, Proceedings of the National Academy of Sciences40, 1018 (1954)

    1954

  8. [8]

    J. W. Hastings and B. M. Sweeney, On the mechanism of temperature independence in a biological clock, Pro- ceedings of the National Academy of Sciences43, 804 (1957)

    work page 1957

Show all 50 references
  1. [9]

    Rombouts, F

    J. Rombouts, F. Tavella, A. Vandervelde, C. Phong, J. E. Ferrell, Q. Yang, and L. Gelens, Mechanistic origins of temperature scaling in the early embryonic cell cycle, Na- ture Communications16, 8045 (2025)

    2025

  2. [10]

    H. Fu, C. Fei, Q. Ouyang, and Y. Tu, Temperature com- pensation through kinetic regulation in biochemical oscil- lators, Proceedings of the National Academy of Sciences 121, e2401567121 (2024)

    2024

  3. [11]

    J. B. Voits and U. S. Schwarz, The generic tempera- ture response of large biochemical networks, PRX Life 3, 043011 (2025)

    2025

  4. [12]

    Jacobs, F

    S. Jacobs, F. Vazquez, N. Frolov, and L. Gelens, Beyond arrhenius: Nonlinear and negative temperature scaling of biological rates from multi-step mechanisms, PRX Life4, 023016 (2026)

    2026

  5. [13]

    Ruoff, Antagonistic balance in the oregonator: About the possibility of temperature-compensation in the Belousov-Zhabotinsky reaction, Physica D: nonlinear phenomena84, 204 (1995)

    P. Ruoff, Antagonistic balance in the oregonator: About the possibility of temperature-compensation in the Belousov-Zhabotinsky reaction, Physica D: nonlinear phenomena84, 204 (1995)

    1995

  6. [14]

    Ginoux and C

    J.-M. Ginoux and C. Letellier, Van der Pol and the his- tory of relaxation oscillations: Toward the emergence of a concept, Chaos: An Interdisciplinary Journal of Non- linear Science22, 023120 (2012)

    2012

  7. [15]

    A. M. Zhabotinsky, Periodic liquid phase reactions, in Proc. Acad. Sci. USSR, Vol. 157 (1964) pp. 392–395

    1964

  8. [16]

    Zaikin and A

    A. Zaikin and A. Zhabotinsky, Concentration wave prop- agation in two-dimensional liquid-phase self-oscillating system, Nature225, 535 (1970)

    1970

  9. [17]

    R. J. Field, E. K¨ or¨ os, and R. M. Noyes, Oscillations in chemical systems. ii. Thorough analysis of temporal oscil- lation in the bromate-cerium-malonic acid system, Jour- nal of the American Chemical Society94, 8649 (1972)

    1972

  10. [18]

    K¨ or¨ os and M

    E. K¨ or¨ os and M. Orb´ an, Uncatalysed oscillatory chemical reactions, Nature273, 371 (1978)

    1978

  11. [19]

    Szalai and E

    I. Szalai and E. K¨ or¨ os, The 1, 4-cyclohexanedione- bromate- acid oscillatory system. 3. Detailed mechanism, The Journal of Physical Chemistry A102, 6892 (1998)

    1998

  12. [20]

    K¨ or¨ os, Monomolecular treatment of chemical oscilla- tion, Nature251, 703 (1974)

    E. K¨ or¨ os, Monomolecular treatment of chemical oscilla- tion, Nature251, 703 (1974)

    1974

  13. [21]

    A. E. Dolbear, The Cricket as a Thermometer, The American Naturalist31, 970 (1897)

  14. [22]

    T. Mair, C. Warnke, K. Tsuji, and S. C. M¨ uller, Con- trol of glycolytic oscillations by temperature, Biophysical Journal88, 639 (2005)

    2005

  15. [23]

    Begasse, M

    M. Begasse, M. Leaver, F. Vazquez, S. Grill, and A. Hy- man, Temperature dependence of cell division timing ac- counts for a shift in the thermal limits ofC. elegansand C. briggsae, Cell Reports10, 647 (2015)

    2015

  16. [24]

    K. C. Mundim, S. Baraldi, H. G. Machado, and F. M. Vieira, Temperature coefficient (Q10) and its applica- tions in biological systems: Beyond the Arrhenius theory, Ecological Modelling431, 109127 (2020)

    2020

  17. [25]

    S. R. Pullela, D. Cristancho, P. He, D. Luo, K. R. Hall, and Z. Cheng, Temperature dependence of the oregona- tor model for the Belousov-Zhabotinsky reaction, Physi- cal Chemistry Chemical Physics11, 4236 (2009)

    2009

  18. [26]

    FitzHugh, Impulses and physiological states in theo- retical models of nerve membrane, Biophysical Journal 1, 445 (1961)

    R. FitzHugh, Impulses and physiological states in theo- retical models of nerve membrane, Biophysical Journal 1, 445 (1961)

    1961

  19. [27]

    Nagumo, S

    J. Nagumo, S. Arimoto, and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proceed- ings of the IRE50, 2061 (1962)

    1962

  20. [28]

    Cebri´ an-Lacasa, P

    D. Cebri´ an-Lacasa, P. Parra-Rivas, D. Ruiz-Reyn´ es, and L. Gelens, Six decades of the FitzHugh–Nagumo model: A guide through its spatio-temporal dynamics and influ- ence across disciplines, Physics Reports1096, 1 (2024)

    2024

  21. [29]

    Krupa and P

    M. Krupa and P. Szmolyan, Relaxation oscillation and canard explosion, Journal of Differential Equations174, 312 (2001)

    2001

  22. [30]

    Desroches, J

    M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. M. Osinga, and M. Wechselberger, Mixed-mode oscillations with multiple time scales, 14 SIAM Review54, 211 (2012)

    2012

  23. [31]

    Kuehn,Multiple time scale dynamics, Applied Math- ematical Sciences, Vol

    C. Kuehn,Multiple time scale dynamics, Applied Math- ematical Sciences, Vol. 191 (Springer, New York, NY, 2015)

    2015

  24. [32]

    J. J. Tyson and P. C. Fife, Target patterns in a realistic model of the Belousov-Zhabotinskii reaction, The Jour- nal of Chemical Physics73, 2224 (1980)

    1980

  25. [33]

    Szalai, E

    I. Szalai, E. K¨ or¨ os, and L. Gy¨ orgyi, 1, 4- cyclohexanedione- bromate- acid oscillatory system. iv. reduced models, The Journal of Physical Chemistry A103, 243 (1999)

    1999

  26. [34]

    Misra, Effect of temperature and associated bifurca- tion in the oscillatory Belousov-Zhabotinskii reaction in a flow reactor, Chemical Physics Letters191, 435 (1992)

    G. Misra, Effect of temperature and associated bifurca- tion in the oscillatory Belousov-Zhabotinskii reaction in a flow reactor, Chemical Physics Letters191, 435 (1992)

    1992

  27. [35]

    G. Nagy, E. K¨ or¨ os, N. Oftedal, K. Tjelflaat, and P. Ruoff, Effect of temperature in cerium-ion-catalyzed bromate- driven oscillators, Chemical Physics Letters250, 255 (1996)

    1996

  28. [36]

    Fujieda and J

    S. Fujieda and J. Kawahito, Thermal behaviour of belousov-zhabotinskii reactions followed by heat ex- change calorimetry involving simultaneous estimation of potentiometric oscillations, Thermochimica Acta183, 153 (1991)

    1991

  29. [37]

    H. C. Oliveira, T. B. Oliveira, and H. Varela, Dinˆ amica oscilat´ oria em sistemas contendo bromato e 1, 4-ciclo- hexanodiona em meio ´ acido: I. efeito da temperatura, Qu ´ ımica Nova35, 348 (2012)

    2012

  30. [38]

    Y. Zhao, S. A. Billings, D. Coca, Y. Guo, R. Ristic, and L. Dematos, Identification of a temperature dependent FitzHugh-Nagumo model for the Belousov-Zhabotinskii reaction, International Journal of Bifurcation and Chaos 21, 3249 (2011)

    2011

  31. [39]

    P. A. Nogueira, H. C. Oliveira, and H. Varela, Time evo- lution of the activation energy in a batch chemical oscil- lator, The Journal of Physical Chemistry A112, 12412 (2008)

    2008

  32. [40]

    B´ ans´ agi Jr, M

    T. B´ ans´ agi Jr, M. Leda, M. Toiya, A. M. Zhabotin- sky, and I. R. Epstein, High-frequency oscillations in the Belousov-Zhabotinsky reaction, The Journal of Physical Chemistry A113, 5644 (2009)

    2009

  33. [41]

    Ruoff, L

    P. Ruoff, L. Rensing, R. Kommedal, and S. Mohsenzadeh, Modeling temperature compensation in chemical and bi- ological oscillators, Chronobiology international14, 499 (1997)

    1997

  34. [42]

    Gelens, K

    L. Gelens, K. C. Huang, and J. Ferrell, J. E., How does theXenopus laevisembryonic cell cycle avoid spatial chaos?, Cell Reports12, 892 (2015)

    2015

  35. [43]

    De Montaigu, A

    A. De Montaigu, A. Giakountis, M. Rubin, R. T´ oth, F. Cremer, V. Sokolova, A. Porri, M. Reymond, C. Weinig, and G. Coupland, Natural diversity in daily rhythms of gene expression contributes to phenotypic variation, Proceedings of the National Academy of Sci- ences112, 905 (2015)

    2015

  36. [44]

    Zhang, Q.-Y

    Z.-B. Zhang, Q.-Y. Wang, Y.-X. Ke, S.-Y. Liu, J.-Q. Ju, W. A. Lim, C. Tang, and P. Wei, Design of tunable oscil- latory dynamics in a synthetic NF-κb signaling circuit, Cell Systems5, 460 (2017)

    2017

  37. [45]

    H.-H. Jo, Y. J. Kim, J. K. Kim, M. Foo, D. E. Somers, and P.-J. Kim, Waveforms of molecular oscillations reveal circadian timekeeping mechanisms, Communications Bi- ology1, 207 (2018)

    2018

  38. [46]

    Tyler, D

    J. Tyler, D. Forger, and J. K. Kim, Inferring causality in biological oscillators, Bioinformatics38, 196 (2021)

    2021

  39. [47]

    S. Gibo, T. Kunihiro, T. Hatsuda, and G. Kurosawa, Waveform distortion for temperature compensation and synchronization in circadian rhythms: An approach based on the renormalization group method, PLOS Com- putational Biology21, e1013246 (2025)

    2025

  40. [48]

    D. B. Forger,Biological clocks, rhythms, and oscillations: The theory of biological timekeeping(MIT Press, 2017)

    2017

  41. [49]

    C. Hong, E. Conrad, and J. Tyson, A proposal for ro- bust temperature compensation of circadian rhythms, Proceedings of the National Academy of Sciences of the United States of America104, 1195 (2007)

    2007

  42. [50]

    Jacobs, Gitlab repository,https:// gitlab.kuleuven.be/gelenslab/publications/ 2026_jacobs_temperature/-/tree/ 6e2f6e838bd809d23070d1a0328f69b87e966287/(2026)

    S. Jacobs, Gitlab repository,https:// gitlab.kuleuven.be/gelenslab/publications/ 2026_jacobs_temperature/-/tree/ 6e2f6e838bd809d23070d1a0328f69b87e966287/(2026)

    2026

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.