In recent years chaos theory has received a great deal of attention among social scientists. Chaos theory originated from turbulent-type of motions in physical systems, but recently its relevance has been explored successfully in economie and social sciences. After a brief overview of recent developments related to chaos theory in economie systems, our paper will present a chaotic model for urb...

In this paper, a novel four-dimensional (4D) autonomous chaotic system is presented. For chaos control of the 4D system, a linear feedback controller only with one variable is designed via matching the variable coefficients of the Lyapunov function, so that the system is no longer chaotic or periodic but globally asymptotically converges to the equilibrium point at the origin. The numerical sim...

We propose a fractional-order WINDMI system, as a generalization of an integer-order system developed by Sprott 2003 . The considered synchronization scheme consists of identical master and slave fractional-order WINDMI systems coupled by linear state error variables. Based on the stability theory of nonlinear fractional-order systems, linear state error feedback control technique is applied to...

This paper deals with the problem of control and synchronization of coupled second-order oscillators showing a chaotic behavior. A classical feedback controller is first used to stabilize the system at its equilibrium. An adaptive observer is then designed to synchronize the states of the master and slave oscillators using a single scalar signal corresponding to an observable state variable of ...

Phase-locked loops (PLLs) are widely used in applications related to control systems and telecommunication networks. Here we show that a single-chain master–slave network of third-order PLLs can exhibit stationary, periodic and chaotic behaviors, when the value of a single parameter is varied. Hopf, period-doubling and saddle–saddle bifurcations are found. Chaos appears in dissipative and non-d...

This Letter presents a robust control scheme for a class of uncertain chaotic systems in the canonical form, with unknown nonlinearities. To cope with the uncertainties, we combine Lyapunov methodology with observer design. The proposed strategy comprises an exponential linearizing feedback and an uncertainty estimator. The developed control scheme allows chaos suppression. The advantage of thi...

We study the simplified control for a novel class of four-dimensional (4-D) fractionalorder chaos in this paper. Firstly, a novel class of 4-D fractional-order chaos is introduced, which can express many actual projects. Secondly, a new simplified controller based on sliding mode theory which needs only one single control input is designed for the control of the proposed class systems. Furtherm...

This chapter deals with the control of chaos exhibited in the behavior of a one-degree-of-freedom impact mechanical oscillator with a single rigid constraint. The mathematical model of such impact oscillator is represented by an impulsive hybrid linear non-autonomous dynamics. The proposed control approach is based chiefly on the OGY method. First, an analytical expression of a constrained cont...