An approach to information propagation in 1-D cellular neural networks. II. Global propagation

For pt.I see P. Thiran et al., ibid., vol.45, no.8, pp.777-89 (1998). This second of two papers studies how and when a global propagation of information, introduced as initial condition, is possible through a one-dimensional (1-D) Cellular Neural Network (CNN) with connections between nearest neighbors only. We will focus on circular arrays, which have the most regular structure, we will show that periodic solutions exist, and we will compute one of them analytically. We will also study their stability.

[1]  Austin Blaquière,et al.  Nonlinear System Analysis , 1966 .

[2]  J. Hale,et al.  Ordinary Differential Equations , 2019, Fundamentals of Numerical Mathematics for Physicists and Engineers.

[3]  A. I. Mees,et al.  Dynamics of feedback systems , 1981 .

[4]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[5]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[6]  J. Mallet-Paret,et al.  The Poincare-Bendixson theorem for monotone cyclic feedback systems , 1990 .

[7]  Leon O. Chua,et al.  CNN cloning template: connected component detector , 1990 .

[8]  L. Chua,et al.  An analytic method for designing simple cellular neural networks , 1991 .

[9]  F. Zou,et al.  Stability of cellular neural networks with opposite-sign templates , 1991 .

[10]  Leon O. Chua,et al.  On the universe of stable cellular neural networks , 1992, Int. J. Circuit Theory Appl..

[11]  Carlo Piccardi,et al.  Bifurcations of limit cycles in periodically forced nonlinear systems: the harmonic balance approach , 1994 .

[12]  Marco Gilli,et al.  Propagation phenomena in cellular neural networks , 1994, Proceedings of the Third IEEE International Workshop on Cellular Neural Networks and their Applications (CNNA-94).

[13]  Leon O. Chua,et al.  Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation , 1995 .

[14]  Leon O. Chua,et al.  Pattern formation properties of autonomous Cellular Neural Networks , 1995 .

[15]  Marco Gilli,et al.  Global dynamic behaviour of a three-cell connected component detector cnn , 1995, Int. J. Circuit Theory Appl..

[16]  Shui-Nee Chow,et al.  Pattern formation and spatial chaos in lattice dynamical systems. II , 1995 .

[17]  Y. Kuznetsov.  Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[18]  Patrick Thiran,et al.  Dynamics and self-organization of locally coupled neural networks , 1996 .

[19]  Patrick Thiran,et al.  An approach to information propagation in cellular neural networks - Part I : Local diffusion , 1998 .