Equilibrium analysis of cellular neural networks

Cellular neural networks are dynamical systems, described by a large set of coupled nonlinear differential equations. The equilibrium point analysis is an important step for understanding the global dynamics and for providing design rules. We yield a set of sufficient conditions (and a simple algorithm for checking them) ensuring the existence of at least one stable equilibrium point. Such conditions give rise to simple constraints, that extend the class of CNN, for which the existence of a stable equilibrium point is rigorously proved. In addition, they are suitable for design and easy to check, because they are directly expressed in term of the template elements

Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems

We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a function of the delay time and external forcing parameters. In particular, we point out that the fixed point solution exhibits a stability island in the two parameter space of time delay and strength of nonlinearity. Significant role played by transients in attaining steady state solutions is pointed out. Various routes to chaos and existence of hyperchaos even for low values of time delay which is evidenced by multiple positive Lyapunov exponents are brought out. The study is extended to the case of two coupled systems, one with delay and the other one without delay.Comment: 34 Pages, 14 Figure

Hopf Bifurcation and Chaos in Tabu Learning Neuron Models

In this paper, we consider the nonlinear dynamical behaviors of some tabu leaning neuron models. We first consider a tabu learning single neuron model. By choosing the memory decay rate as a bifurcation parameter, we prove that Hopf bifurcation occurs in the neuron. The stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory. We give a numerical example to verify the theoretical analysis. Then, we demonstrate the chaotic behavior in such a neuron with sinusoidal external input, via computer simulations. Finally, we study the chaotic behaviors in tabu learning two-neuron models, with linear and quadratic proximity functions respectively.Comment: 14 pages, 13 figures, Accepted by International Journal of Bifurcation and Chao

A Model for VLSI implementation of CNN image processing chips using current-mode techniques

A new Cellular Neural Network model is proposed which allows simpler and faster VLSI implementation than previous models. Current-mode building blocks are presented for the design of CMOS image preprocessing chips (feature extraction, noise filtering , compound component detection, etc.) using the cellular neural network paradigm. Area evaluation for the new model shows a reduction off about 50% as compared to the use of current-mode techniques with conventional models. Experimental measurements of CMOS prototypes designed in a 1.6 μm n-well double-metal single-poly technology are reported

Existence and Stability of Standing Pulses in Neural Networks : I Existence

We consider the existence of standing pulse solutions of a neural network integro-differential equation. These pulses are bistable with the zero state and may be an analogue for short term memory in the brain. The network consists of a single-layer of neurons synaptically connected by lateral inhibition. Our work extends the classic Amari result by considering a non-saturating gain function. We consider a specific connectivity function where the existence conditions for single-pulses can be reduced to the solution of an algebraic system. In addition to the two localized pulse solutions found by Amari, we find that three or more pulses can coexist. We also show the existence of nonconvex ``dimpled'' pulses and double pulses. We map out the pulse shapes and maximum firing rates for different connection weights and gain functions.Comment: 31 pages, 29 figures, submitted to SIAM Journal on Applied Dynamical System