Wave propagation in RTD-based cellular neural networks

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• 作者：Hsu ; Cheng-Hsiung ; Yang ; Suh-Yuh
• 关键词：34B15 ; 34B45 ; 34K10 ; 34K28 ; Lattice dynamical systems ; RTD-based cellular neural networks ; Discrete Fisher equation ; Discrete Nagumo equation ; Monotone iteration methods ; Traveling waves ; Standing waves
• 刊名：Journal of Differential Equations
• 出版年：2004
• 出版时间：September 20, 2004
• 年：2004
• 卷：204
• 期：2
• 页码：339-379
• 全文大小：2.02 M

文摘

This work investigates the existence of monotonic traveling wave and standing wave solutions of RTD-based cellular neural networks in the one-dimensional integer lattice Z¹. For nonzero wave speed c, applying the monotone iteration method with the aid of real roots of the corresponding characteristic function of the profile equation, we can partition the parameter space (γ,δ)-plane into four regions such that all the admissible monotonic traveling wave solutions connecting two neighboring equilibria can be classified completely. For the case of c=0, a discrete version of the monotone iteration scheme is established for proving the existence of monotonic standing wave solutions. Furthermore, if γ or δ is zero then the profile equation for the standing waves can be viewed as an one-dimensional iteration map and we then prove the multiplicity results of monotonic standing waves by using the techniques of dynamical systems for maps. Some numerical results of the monotone iteration scheme for traveling wave solutions are also presented.