Abstract
Using the averaging theory we study the periodic solutions and their linear stability of the $3$--dimensional chaotic quadratic polynomial differential systems without equilibria studied in [3]. All these differential systems depend only on one--parameter.
Highlights
Finding periodic orbits of differential systems takes an important place in the study of the behavior of the trajectories of a given differential system
After the equilibrium points, the periodic orbits and their kind of stability provide many information on the dynamics of a differential system, mainly when the system under study models a real problem coming from biology, physics, engineering, etc
Our goal is to apply the averaging theory in order to study the periodic orbits of such differential systems when the parameter a is sufficiently small
Summary
Finding periodic orbits of differential systems takes an important place in the study of the behavior of the trajectories of a given differential system. In this paper our goal is to apply such approach in order to study the periodic orbits of some families of chaotic differential systems by varying a small specific parameter in a convenient way. We study the occurrence of periodic orbits from a list of chaotic quadratic polynomial differential systems in R3 provided by Jafari, Sprott and Golpayeganiin [3]. Our goal is to apply the averaging theory in order to study the periodic orbits of such differential systems when the parameter a is sufficiently small. LLIBRE AND D.J. TONON other words we study the codimension one bifurcation of periodic orbits from those chaotic system differential systems, that is, we provide sufficient conditions in order that some of the systems N Ei, i = 1, . It is easy to check that the periodic solutions described in Theorem 1 exist when the corresponding differential system have no equilibria, except for system (iii) and (xi) that when the periodic solution exists there are equilibria
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