## Cellular neural networks: theory and applicationsThis book deals with new theoretical results for studyingCellular Neural Networks (CNNs) concerning its dynamical behavior. Newaspects of CNNs' applications are developed for modelling of somefamous nonlinear partial differential equations arising in biology, genetics, neurophysiology, physics, ecology, etc. The analysis ofCNNs' models is based on the harmonic balance method well known incontrol theory and in the study of electronic oscillators. Suchphenomena as hysteresis, bifurcation and chaos are studied for CNNs.The topics investigated in the book involve several scientificdisciplines, such as dynamical systems, applied mathematics, mathematical modelling, information processing, biology andneurophysiology. The reader will find comprehensive discussion on thesubject as well as rigorous mathematical analyses of networks ofneurons from the view point of dynamical systems. The text is writtenas a textbook for senior undergraduate and graduate students inapplied mathematics. Providing a summary of recent results on dynamicsand modelling of CNNs, the book will also be of interest to allresearchers in the area. |

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### Contents

Mathematical Point of View | 23 |

Stability Analysis of Bidirectional Associative | 59 |

On the Dynamics of Some Classes of Cellular Neural Networks | 77 |

Copyright | |

4 other sections not shown

### Other editions - View all

Cellular Neural Networks: Theory and Applications Angela Slavova,Valeri Mladenov Limited preview - 2004 |

### Common terms and phrases

4th Int algorithm analog approximation architecture array assume asymptotic stability autonomous boundary conditions Budapest Budapest Hungary capacitor Cellular Neural Networks Chua's circuits Circuit Theory Circuits and Systems Circuits Syst cloning template CNN cell CNN Universal Machine CNN-based CNN's coefficients complete stability consider constant continuous functions corresponding coupled denotes differential equations discrete discrete space eigenvalues equilibrium point feedback FitzHugh-Nagumo equation flux fuzzified global asymptotic stability grid heat transfer Hopfield Hopfield Networks IEEE IEEE Trans image processing implementation initial conditions input Kostic L. O. Chua L.O.Chua Lyapunov function M-matrix matrix method mode neurons node nonsingular M-matrix obtained order cells output parameters pattern formation PDEs periodic solutions piecewise linear predicted Proc programming realized Reljin resistor Roska Seville Spain shortest path Simulation solving structure symmetric temporal eigenvalues Theorem trajectory travelling wave solutions Turing Patterns two-dimensional values variables vector voltage wave propagation Workshop CNNA-96 zero