The authors prove existence of travelling pulses in a toxicity-extended Klausmeier model by constructing homoclinic orbits via geometric singular perturbation theory in an asymptotic scaling regime and validate against numerics.
Journal of Mathematical Biology 51(2), 183–197 (2005)
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A four-PDE model shows that inter- and intra-specific plant-soil feedbacks can produce coexistence, single-species dominance, or spatial vegetation patterns depending on parameter values.
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Far-from-equilibrium travelling pulses in sloped semi-arid environments driven by autotoxicity effects
The authors prove existence of travelling pulses in a toxicity-extended Klausmeier model by constructing homoclinic orbits via geometric singular perturbation theory in an asymptotic scaling regime and validate against numerics.
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Modeling competitive interactions and plant-soil feedback in vegetation dynamics
A four-PDE model shows that inter- and intra-specific plant-soil feedbacks can produce coexistence, single-species dominance, or spatial vegetation patterns depending on parameter values.