Abstract
The paper concerns the problem of synchronization-control in nonlinear bacterial cultures reaction-diffusion model, linear and nonlinear controllers have been proposed to study the complete synchronization of couples of the Degn-Harrison system with identical and non-identical coefficients. Throughout the paper, we use numerical simulation to show the effectiveness of the proposed results.
Highlights
Synchronization is a process of controlling the output of the response system to force its behavior to follow that of the corresponding drive system asymptotically
Synchronizing in high-dimensional systems modeled in the spatial-temporal domain and described by nonlinear reaction-diffusion systems which state variables depend on the time and spatial position stills in its initial stage
Reaction-diffusion systems models act a central role in describing the phenomena that exist in neuronal networks, chemical reaction systems, image processing and ecosystems
Summary
Synchronization is a process of controlling the output of the response system (slave system) to force its behavior to follow that of the corresponding drive system (master system) asymptotically. The present paper deals with the analysis of control synchronization for bacterial culture model introduced by Degn and Harrison [23] as. F. Mesdoui et al.: Synchronization Methods for the Degn-Harrison Reaction-Diffusion Systems where u1(x, t), u2(x, t) represent the oxygen and the nutrient respectively, a, b, d1, d2, k are positive constants and gk (u1). The Degn-Harrison model (1) is used to describe the effect of the oxygen concentration in the Klebsiella aerogenes bacteria culture, for a more detailed background of chemical reaction scheme and significance of system (1) we refer interested reader to [24], [25]. The contribution of this paper is the development of novel methods for synchronization of Degn-Harrison reaction-diffusion system with identical or non-identical coefficients.
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