Complex Dynamics and Cellular Neural Networks

2001 ◽  
pp. 135-168
Author(s):  
Luigi Fortuna ◽  
Gianguido Rizzotto ◽  
Mario Lavorgna ◽  
Giuseppe Nunnari ◽  
M. Gabriella Xibilia ◽  
...  
Keyword(s):  
Neural Networks ◽  
Complex Dynamics ◽  
Cellular Neural Networks

FOURTH-ORDER NEARLY-SYMMETRIC CNNS EXHIBITING COMPLEX DYNAMICS

2005 ◽  
Vol 15 (05) ◽  
pp. 1579-1587 ◽  
Author(s):  
M. DI MARCO ◽  
M. FORTI ◽  
M. GRAZZINI ◽  
L. PANCIONI
Keyword(s):  
Dynamical System ◽  
Neural Networks ◽  
Fourth Order ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Cellular Neural Networks ◽  
Parameter Family ◽  
Relative Errors ◽  
Period Doubling Bifurcations

In this paper, the possible presence of complex dynamics in nearly-symmetric standard Cellular Neural Networks (CNNs), is investigated. A one-parameter family of fourth-order CNNs is presented, which exhibits a cascade of period-doubling bifurcations leading to the birth of a complex attractor, close to some nominal symmetric CNN. Different from previous work on this topic, the bifurcations and complex dynamics are obtained for small relative errors with respect to the nominal interconnections. The fourth-order CNNs have negative (inhibitory) interconnections between distinct neurons, and are designed by a variant of a technique proposed by Smale to embed a given dynamical system within a competitive dynamical system of larger order.

BIFURCATIONS AND CHAOS IN CELLULAR NEURAL NETWORKS

2003 ◽  
Vol 12 (04) ◽  
pp. 417-433 ◽  
Author(s):  
M. BIEY ◽  
P. CHECCO ◽  
M. GILLI
Keyword(s):  
Neural Networks ◽  
Bifurcation Analysis ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Cellular Neural Networks ◽  
Two Dimensional ◽  
First Order ◽  
Stable Periodic ◽  
Torus Breakdown

The dynamic behavior of first-order autonomous space invariant cellular neural networks (CNNs) is investigated. It is shown that complex dynamics may occur in very simple CNN structures, described by two-dimensional templates that present only vertical and horizontal couplings. The bifurcation processes are analyzed through the computation of the limit cycle Floquet's multipliers, the evaluation of the Lyapunov exponents and of the signal spectra. As a main result a detailed and accurate two-dimensional bifurcation diagram is reported. The diagram allows one to distinguish several regions in the parameter space of a single CNN. They correspond to stable, periodic, quasi-periodic, and chaotic behavior, respectively. In particular it is shown that chaotic regions can be reached through two different routes: period doubling and torus breakdown. We remark that most practical CNN implementations exploit first order cells and space-invariant templates: so far only a few examples of complex dynamics and no complete bifurcation analysis have been presented for such networks.

COMPLEX DYNAMICS IN NEARLY SYMMETRIC THREE-CELL CELLULAR NEURAL NETWORKS

2002 ◽  
Vol 12 (06) ◽  
pp. 1357-1362 ◽  
Author(s):  
M. DI MARCO ◽  
M. FORTI ◽  
A. TESI
Keyword(s):  
Neural Networks ◽  
Computer Simulations ◽  
Complex Dynamics ◽  
Small Neighborhood ◽  
Period Doubling ◽  
Cellular Neural Networks ◽  
Third Order ◽  
Major Point ◽  
Large Size ◽  
Period Doubling Bifurcations

The paper introduces a class of third-order nonsymmetric Cellular Neural Networks (CNNs), and shows through computer simulations that they undergo a cascade of period doubling bifurcations which leads to the birth of a large-size complex attractor. A major point is that these bifurcations and complex dynamics happen in a small neighborhood of a particular CNN with a symmetric interconnection matrix.

New Criteria on Stability of Dynamic Memristor Delayed Cellular Neural Networks

2020 ◽  
pp. 1-13
Author(s):  
Kun Deng ◽  
Song Zhu ◽  
Wei Dai ◽  
Chunyu Yang ◽  
Shiping Wen
Keyword(s):  
Neural Networks ◽  
Cellular Neural Networks ◽  
New Criteria

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

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