Spatiotemporal Chaos in Glow Discharge-Semiconductor Systems

Abstract

Entrainment of limit cycles by chaos [1] is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach [2], it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [3].Spatiotemporal chaos is one of the complicated structures observed in spatially extended dynamical systems and it is characterized by chaotic properties both in time and space coordinates. The existence of a positive Lyapunov exponent can be used to detect spatiotemporal complexity, which can be observed, for example, in liquid crystal light valves, electroconvection, cardiac fibrillation, chemical reaction-diffusion systems and fluidized granular matter. Spatially extended dynamical systems often serve as standard models for the investigation of complex phenomena in electronics. A special interest is directed towards pattern-formation phenomena in electronic media, mainly the nonlinear gas discharge systems. It is clear that chaos can appear as an intrinsic property of systems as well as through couplings. The interaction of spatially extended systems is important for neural networks, reentry initiation in coupled parallel fibers, thermal convection in multilayered media and for systems consisting of several weakly coupled spatially extended systems such as the electrohydrodynamical convection in liquid crystals. In the present study, we numerically verify the appearance of cyclic irregular behavior (entrainment by * Corresponding Author chaos) in unidirectionally coupled glow discharge-semiconductor systems. The chaos in the response system is obtained through period-doubling cascade of the drive system such that it admits infinitely many unstable periodic solutions and sensitivity is present. Previously, the extension of chaos through couplings has been considered by synchronization[2], [4]- [9]. The task is difficult for partial differential equations because of the choice of connecting parameters [10]- [12]. Kocarev et al. [10] suggested a useful time-discontinuous monitoring for synchronization, but our choice is based on a finite dimensional connection.It is demonstrated that the present results cannot be reduced to any one in the theory of synchronization of chaos. The technique of chaos extension suggested in the present research can be related to technical problems [13,14], where collectives of microdischarge systems are considered and in models which appear in neural networks, hydrodynamics, optics, chemical reactions and electrical oscillators. Sta...