In this paper, a reaction system consisting of two parallel, non-isothermal autocatalytic reactions in a Continuous Stirred Tank Reactor (CSTR) has been considered. Reactor chaotic behavior is possible for certain values of system parameters. Two types of controllers are designed and compared in order to control both the reactor temperature and the product concentration. T...

We introduce a novel approach for controlling fast chaos in time-delay dynamical systems and use it to control a chaotic photonic device with a characteristic time scale of approximately 12 ns. Our approach is a prescription for how to implement existing chaos-control algorithms in a way that exploits the system's inherent time delay and allows control even in the presence of substantial contro...

The properties of nonlinear dynamics and chaos are shown to be fundamental to optimal communication signals subject to two practical and realistic design requirements: (i) operation in a noisy environment and (ii) simple hardware implementation. Starting with a simple electronic circuit, a linear filter receiver is presumed, and the matched optimal communication waveform that maximizes the rece...

In Part I ([9], this journal), Li and McLaughlin proved the existence of homoclinic orbits in certain discrete NLS systems. In this paper, we will construct Smale horseshoes based on the existence of homoclinic orbits in these systems. First, we will construct Smale horseshoes for a general high dimensional dynamical system. As a result, a certain compact, invariant Cantor set3 is constructed. ...

Chaos, control, anticontrol and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governor and spring for which time-delay effect is considered are studied in the paper. By applying numerical results, phase diagram and power spectrum are presented to observe periodic and chaotic motions. Linear feedback control and adaptive control algorithm are u...

It is well known that most conventional control methods and many special techniques can be used for chaos control [Chen & Dong, 1998] whether the purpose is to reduce “bad” chaos or to introduce “good” chaos. Numerous control methodologies have been proposed, developed, tested and applied. Due to its great potential in nontraditional applications such as those found within the context of physic...

Chaos control exploits the sensitivity to initial conditions and to perturbations that is inherent in chaos as a means to stabilize unstable periodic orbits within a chaotic attractor. The control can operate by altering system variables or system parameters, and either by discrete corrections or by continuous feedback. Many methods of chaos control have been derived and tested [Chen & Dong, 19...

Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott}Grebogi}Yorke (OGY) method and the adaptive method. We also discuss a series of relevant issues connected with chaos con...

This paper investigates the adaptive chaos control and synchronization of the Shaw chaotic system (Shaw, 1981) with unknown parameters. First, we design adaptive control laws to stabilize the Shaw chaotic system with unknown parameters to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Next, we derive adaptive control laws to achieve gl...