Hopf and zip bifurcation in a specific (n+1)-dimensional competitive system

In this work we study the occurrence of Andronov-Hopf and zip bifurcation in a concrete (n + 1)-dimensional predator-prey system modelling the competition among n species of predators for one species of prey. This is a generalization of results by Farkas (1984

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No presente trabalho estudaremos a ocorrência do fenômeno de bifurcação zip e de bifurcação de Andronov-Hopf, num modelo matemático dado por um sistema de equações diferenciais parciais que descreve a dinâmica entre n predadores competindo por uma presanot availabl

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Neste trabalho mostramos a ocorrência de bifurcação de Hopf em dois modelos epidemiológicos, que descrevem doenças micro e macro parasíticas, cada um representado por um sistema de equações diferenciais ordinárias no plano. Além disso, estudamosa existência e unicidade de órbitas periódicas, via teoria de Liénard. Para finalizar, interpretamos os resultados obtidos, para descrever o comportamento da doençaWe show here the occurrence of Hopf bifurcation in two epidemiological models, describing micro and macro parasitical diseases, each model represented by a system of ordinary differential equations in the plane. Furthermore, we study theexistenceand unicity of periodic orbits, via liénard's theory. Finally, we interpret the results we obtained, to describe the behavior of the disease

Normal Hyperbolicity and Continuity of Global Attractors for a Nonlocal Evolution Equations

We show the normal hyperbolicity property for the equilibria of the evolution equation ( , )/ = − ( , ) + ( * ( , ) + ℎ), ℎ, ≥ 0, and using the normal hyperbolicity property we prove the continuity (upper semicontinuity and lower semicontinuity) of the global attractors of the flow generated by this equation, with respect to functional parameter

Normal Hyperbolicity and Continuity of Global Attractors for a Nonlocal Evolution Equations

We show the normal hyperbolicity property for the equilibria of the evolution equation ∂m(r,t)/∂t=-m(r,t)+g(βJ*m(r,t)+βh),  h,β≥0, and using the normal hyperbolicity property we prove the continuity (upper semicontinuity and lower semicontinuity) of the global attractors of the flow generated by this equation, with respect to functional parameter J