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This paper addresses the stabilization problem of a class of fractional order chaotic systems. The analytically obtained control structure, derived by blending the systematic backstepping procedure with Mittag-Leffler and Lyapunov stability results, helps in obtaining stability of a special case of strict feedback class of fractional order chaotic systems and at the same time avoids the singularity problem. The stabilizing controller is derived for a class of three dimensional systems which can be expressed in strict-feedback form. Thereafter, the methodology has been applied to two example systems i.e. chaotic Lorenz system and Lü system belonging to the addressed class to show the application of results. Numerical simulation results given at the end confirm the efficacy of the scheme presented here. [ABSTRACT FROM AUTHOR]

In the present paper, the synchronization by the Ge-Yao-Chen (GYC) partial region stability theory of chaotic Mathieu-Van der Pol and chaotic Duffing-Van der Pol systems with fractional order-derivative is proposed. Numerical simulations show that this synchronization technique is very effective and it turns out that the fractional order-derivative induces quick synchronization compared to integer order-derivative of these systems. In order to bring out the chaotic behavior of these systems either with fractional or with integer order-derivative, we simulate their phase portraits and the Lyapunov exponent. Moreover, we provide in this work an approximated solution to both systems to show that the solution of such a system can be represented as a simple power-series function. Furthermore, the representation of the error dynamics with respect to the time before and after the control action approves the effectiveness of the control method and proves the possibility of stabilization and controllability of chaotic systems with an appropriate. Furthermore, the synchronization of the fractional Mathieu-Van der Pol system using the fractional Duffing-Van der Pol system is simulated. [ABSTRACT FROM AUTHOR]

A discrete predator-prey system with square root functional response is presented. We study the existence and local stability analysis of the system. The conditions of existence of flip and Niemark-Sacker bifurcations in the system are derived. Furthermore, the chaotic behavior of the system in the sense of Marotto is proved. Numerical simulations are performed to show the consistence with analytical results and also to exhibit the complexity of the system. Finally, chaos control in the system is achieved via OGY feedback control method. [ABSTRACT FROM AUTHOR]

This paper considers a mixed duopoly competition model, in which two enterprises produce heterogeneous commodities and compete for output in the same market. One enterprise separates the ownership from the management rights, and the enterprise owner entrusts a manager to manage the enterprise. The other enterprise considers consumer surplus. Through stability theory and numerical simulation, the local stability of each equilibrium point and the way the system performs bifurcation are analyzed. By using the basin of attraction, the global stability of the system is studied. The multistability is explained and the properties and some phenomena of the basin of attraction and the chaotic attractor are analyzed by using the knowledge of noninvertible map and critical curve. Finally, the influence of parameters on enterprise profit and objective is also analyzed, which is helpful for enterprises to make decisions in the process of game. • A mixed duopoly Cournot competition model is established based on heterogeneous products. • The complex dynamic behavior of the economic system is analyzed by means of chaos theory and numerical simulation. • The complex structures of the basin of attraction and chaotic attractor are studied by using noninvertible map. • The influence of the parameters on the average objective and the average profit of the two enterprises is analyzed. [ABSTRACT FROM AUTHOR]