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Waves analysis and spatiotemporal pattern formation of an ecosystem model. (English) Zbl 1228.35033
For the predator-prey model expressing conservation of population densities the author proves the existence and boundedness of the global solution. Using the upper and lower solutions method, conditions for the existence of positive steady state solutions are derived. Then, the local stability of non-negative steady states is established, and with the aid of a Lyapunov function the global asymptotic stability of endemic equilibrium is obtained. Besides the proof of the existence of travelling wave solutions, complex patterns formation arising from Hopf and Turing instabilities is analyzed, and the emergence of spatio-temporal chaos is numerically investigated.
MSC:
35B32Bifurcation (PDE)
35K57Reaction-diffusion equations
35B35Stability of solutions of PDE
35B36Pattern formation in solutions of PDE
35Q92PDEs in connection with biology and other natural sciences
92D25Population dynamics (general)
35C07Traveling wave solutions of PDE
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