MLC Circuit in the Frame of CNN

Abstract

A CNN-based nonautonomous chaotic oscillator circuit design is presented. Murali–Lakshmanan–Chua circuit, known as MLC circuit, is modeled by using CNN cells. The circuit implementation is supported by an eigenvalue study of the introduced system. The proposed model gives an alternative to MLC circuit with inductorless RC-based circuit realization.

Lorenz-like system design using cellular neural networks

“…The primary disadvantage of the SC-CNN-based systems is the representation of system nonlinearity using only one state variable [10][11][12]. The output function of the SC-CNN expressed in Eq.…”

Dynamics of SC-CNN Based Variant of MLC Circuit: An Experimental Study

“…This new version that exploits an analog architecture of CNN, known as State Controlled-CNN (SC-CNN) has been designed for both autonomous and nonautonomous systems by the same authors [Arena et al, 1995a[Arena et al, , 1996Gunay et al, 2005b;Buscarino et al, 2009a;Gunay, 2010]. The name of this SC-CNN model is due to the fact that it is basically equal to the linear CNN model [Chua, 1998] with the addition of the state template.…”

“…The advantages of SC-CNN are that, this alternative realization is an inductorless and RC based circuitry, thereby leading itself to easy hardware realization, compactness as well as VLSI implementation. A large number of electronic implementations of CNN concept and their applications using both autonomous and nonautonomous nonlinear electronic circuits systems were made during the past two decades by several researchers [Arena et al, 1995a[Arena et al, , 1996Gunay et al, 2005b;Buscarino et al, 2009a;Gunay, 2010]. Much recent work has been motivated by the application of CNN based circuits to communications [Gunay et al, 2003;Kilic et al, 2004], neural dynamics [Cao et al, 2010], etc.…”

“…From this point of view, classical configuration of nonautonomous circuit, such as MLC circuit [Murali et al, 1994], and its variant circuit [Thamilmaran & Lakshmanan, 2002] are studied. The CNN based nonautonomous chaotic circuits have been introduced very few both numerically and experimentally in the nonlinear dynamics literature and references therein [Buscarino et al, 2009a;Gunay, 2010]. Based on this, recently, Buscarino et al [2009b] and Gunay [2010], have designed a CNN formulation using nonautonomous circuits for generating chaos using just two generalized CNN cells.…”

“…The CNN based nonautonomous chaotic circuits have been introduced very few both numerically and experimentally in the nonlinear dynamics literature and references therein [Buscarino et al, 2009a;Gunay, 2010]. Based on this, recently, Buscarino et al [2009b] and Gunay [2010], have designed a CNN formulation using nonautonomous circuits for generating chaos using just two generalized CNN cells. The earlier cited work on CNN based Murali-Lakshmanan-Chua (MLC) circuit that built up the complex network, by using two generalized cells, reported that the dynamics of nonautonomous nonlinear system namely MLC circuit is a dissipative two-dimensional series LCR circuit with Chua's diode as its only nonlinear element introduced by Murali et al [1994].…”