In order to further understand a complex 3D dynamical system showing strange chaotic attractors with two stable node-foci near Hopf bifurcation point, we propose nonlinear control scheme to the system and the controlled system, depending on five parameters, can exhibit codimension one, two, and three Hopf bifurcations in a much larger parameter regain. The control strategy used keeps the equili...

We study the one-dimensional logistic map with control parameter perturbed by a small periodic function. In the pure constant case, scaling arguments are used to obtain the exponents related to the relaxation of the trajectories at the exchange of stability, period-doubling and tangent bifurcations. In particular, we evaluate the exponent z which describes the divergence of the relaxation time ...

In this paper, a periodic parametric perturbation was designed for controlling chaos and generating chaos (chaotification) from a three-dimensional autonomous system. When we added the small periodic parametric perturbations, the system became a non-autonomous system, which has abundant dynamics behavior. Periodic, chaotic and hyperchaos behaviors were identified by the Lyapunov exponents and b...

The method of harmonic linearization, numerical methods, and the applied bifurcation theory together discover new opportunities for analysis of hidden attractors of control systems. In the present paper these opportunities are demonstrated. New analytical-numerical method based on the above-mentioned technique is discussed. Application of this technique for hidden attractor localization of gene...

A mathematical model describing the dynamics  of a  delayed  stage structure prey - predator  system  with  prey  refuge  is  considered.  The  existence,  uniqueness  and bounded- ness  of  the  solution  are  discussed.    All  the  feasibl e  equilibrium  points  are determined.  The   stability  analysis  of  them  are  investigated.  By  employ ing  the time delay as the bifurcation parame...

This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence and saturated treatment rate. The existence stability analysis equilibria have been investigated. It has shown that the disease free equilibrium point (DFE) is globally asymptotically stable if basic reproduction number less than unity transmission infection some threshold. system exhi...

In this paper, dynamical analysis is presented for a group of unicycles in leader-follower formation. The equilibrium formations were characterized along with the local stability analysis. It was demonstrated that with the variation in control gain, the collective dynamics might undergo Andronov-Hopf and Fold-Hopf bifurcations. An increase in the number of unicycles increase the vigor of quasi-...

We discuss new and improved algorithms for the bifurcation analysis of fixed points and periodic orbits (cycles) of maps and their implementation in matcont, a matlab toolbox for continuation and bifurcation analysis of dynamical systems. This includes the numerical continuation of fixed points of iterates of the map with one control parameter, detecting and locating their bifurcation points (i...

We consider the delayed feedback control of a torsion-free unstable periodic orbit originated in a dynamical system at a subcritical Hopf bifurcation. Close to the bifurcation point the problem is treated analytically using the method of averaging. We discuss the necessity of employing an unstable degree of freedom in the feedback loop as well as a nonlinear coupling between the controlled syst...