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

Xiaoliang Xie, Wen Zhang (2017)

Open Mathematics

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....

Hopf-like bifurcations in planar piecewise linear systems.

Emilio Freire, Enrique Ponce, Francisco Torres (1997)

Publicacions Matemàtiques

Continuous planar piecewise linear systems with two linear zones are considered. Due to their low differentiability specific techniques of analysis must be developed. Several bifurcations giving rise to limit cycles are pointed out.

Hoptf bifurcation from infinity for planar control systems.

Jaume Llibre, Enrique Ponce (1997)

Publicacions Matemàtiques

Symmetric piecewise linear bi-dimensional systems are very common in control engineering. They constitute a class of non-differentiable vector fields for which classical Hopf bifurcation theorems are not applicable. For such systems, sufficient and necessary conditions for bifurcation of a limit cycle from the periodic orbit at infinity are given.

Impulsive periodic boundary value problem

Jan Draessler (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In the paper we consider the impulsive periodic boundary value problem with a general linear left hand side. The results are based on the topological degree theorems for the corresponding operator equation ( I - F ) u = 0 on a certain set Ω that is established using properties of strict lower and upper functions of the boundary value problem.

Impulsive stabilization and synchronization of uncertain financial hyperchaotic systems

Song Zheng (2016)

Kybernetika

In this paper the issue of impulsive stabilization and synchronization of uncertain financial hyperchaotic systems with parameters perturbation is investigated. Applying the impulsive control theory, some less conservative and easily verified criteria for the stabilization and synchronization of financial hyperchaotic systems are derived. The control gains and impulsive intervals can be variable. Moreover, the boundaries of the stable region are also estimated according to the equidistant impulse...

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