Fixed Points and Stability of Stochastic Neutral Partial Differential Equations with Infinite Delays

2009 ◽  
Vol 27 (6) ◽  
pp. 1163-1173 ◽  
Author(s):  
Jiaowan Luo ◽  
Takeshi Taniguchi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fixed Points ◽  
Partial Differential ◽  
Infinite Delays

CHAOTIC BEHAVIOR AND CHAOS CONTROL FOR A CLASS OF COMPLEX PARTIAL DIFFERENTIAL EQUATIONS

2001 ◽  
Vol 12 (06) ◽  
pp. 889-899 ◽  
Author(s):  
G. M. MAHMOUD ◽  
H. A. ABDUSALAM ◽  
A. A. M. FARGHALY
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fixed Points ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Point Of View ◽  
Partial Differential ◽  
Ginzburg Landau ◽  
Practical Point ◽  
Nagumo Equations

Systems of complex partial differential equations, which include the famous nonlinear Schrödinger, complex Ginzburg–Landau and Nagumo equations, as examples, are important from a practical point of view. These equations appear in many important fields of physics. The goal of this paper is to concentrate on this class of complex partial differential equations and study the fixed points and their stability analytically, the chaotic behavior and chaos control of their unstable periodic solutions. The presence of chaotic behavior in this class is verified by the existence of positive maximal Lyapunov exponent.The problem of chaos control is treated by applying the method of Pyragas. Some conditions on the parameters of the systems are obtained analytically under which the fixed points are stable (or unstable).

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