On a Stochastic Coupled System of Reaction-Diffusion of Nonlocal Type

2014 ◽  
pp. 301-320
Author(s):  
E. A. Coayla-Teran ◽  
J. Ferreira ◽  
P. M. D. de Magalhães ◽  
H. B. de Oliveira
Keyword(s):  
Reaction Diffusion ◽  
Coupled System

Observer-based output feedback control design for a coupled system of fractional ordinary and reaction–diffusion equations

2020 ◽  
Author(s):  
Shadi Amiri ◽  
Mohammad Keyanpour ◽  
Asadollah Asaraii
Keyword(s):  
Differential Equation ◽  
Output Feedback ◽  
Closed Loop ◽  
Output Feedback Control ◽  
Reaction Diffusion ◽  
Coupled System ◽  
Reaction Diffusion Equations ◽  
Backstepping Method ◽  
Neumann Type ◽  
Fractional Reaction

Abstract In this paper, we investigate the stabilization problem of a cascade of a fractional ordinary differential equation (FODE) and a fractional reaction–diffusion (FRD) equation where the interconnections are of Neumann type. We exploit the partial differential equation backstepping method for designing a controller, which guarantees the Mittag–Leffler stability of the FODE-FRD cascade. Moreover, we propose an observer that is Mittag–Leffler convergent. Also, we propose an output feedback boundary controller, and we prove that the closed-loop FODE-FRD system is Mittag–Leffler stable in the sense of the corresponding norm. Finally, numerical simulations are presented to verify the results.

OSCILLATIONS ON THE EDGE OF CHAOS VIA DISSIPATION AND DIFFUSION

2007 ◽  
Vol 17 (05) ◽  
pp. 1531-1573 ◽  
Author(s):  
MAKOTO ITOH ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Reaction Diffusion ◽  
Coupled System ◽  
Reaction Diffusion Equations ◽  
Nonlinear Dynamical ◽  
Edge Of Chaos ◽  
Secondary Purpose ◽  
Spatio Temporal ◽  
And Diffusion

The primary purpose of this paper is to show that simple dissipation can bring about oscillations in certain kinds of asymptotically stable nonlinear dynamical systems; namely when the system is locally active where the dissipation is introduced. Furthermore, if these nonlinear dynamical systems are coupled with appropriate choice of diffusion coefficients, then the coupled system can exhibit spatio-temporal oscillations. The secondary purpose of this paper is to show that spatio-temporal oscillations can occur in spatially discrete reaction diffusion equations operating on the edge of chaos, provided the array size is sufficiently large.

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