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Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses

100%

Fečkan M., Wang J., Zhou Y.

Nonautonomous Dynamical Systems

2014

tom 1

nr 1

In this paper, we consider periodic solutions for a class of nonlinear evolution equations with non-instantaneous impulses on Banach spaces. By constructing a Poincaré operator, which is a composition of the maps and using the techniques of a priori estimate, we avoid assuming that periodic solution is bounded like in [1-4] and try to present new sufficient conditions on the existence of periodic mild solutions for such problems by utilizing semigroup theory and Leray-Schauder's fixed point theorem. Furthermore, existence of a global compact connected attractor for the Poincaré operator is derived.

Hopf bifurcations in a three-species food chain system with multiple delays

100%

Xie X., Zhang W.

Open Mathematics

2017

tom 15

nr 1

508-519

This paper is concerned with a three-species Lotka-Volterra food chain system with multiple delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the stability of the positive equilibrium and existence of Hopf bifurcations are investigated. Furthermore, the direction of bifurcations and the stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.

Ograniczanie wyników

1 Nonautonomous Dynamical Systems

1 Open Mathematics

1 Fečkan M.

1 Wang J.

1 Xie X.

1 Zhang W.

1 Zhou Y.

1 2017

1 2014

Wyniki wyszukiwania

Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses

Hopf bifurcations in a three-species food chain system with multiple delays