## 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

1 | |

Theory of Cellular Neural Networks Mathematical Point of View | 23 |

Stability Analysis of Bidirectional Associative Memory Cellular Neural Networks with Time Delays | 59 |

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

SpatioTemporal Phenomena in Two dimensional Cellular Nonlinear Networks | 97 |

Travelling Waves in FitzHughNagumo Cellular Neural Network Model | 113 |

CNN Applications in Modeling and Solving NonElectrical Problems | 135 |

Cellular Neural Networks for Obstacle Detection in Stereo Vision Imagery | 173 |

Object Tracking and Exact Colour Reproduction for Medical Imaging | 181 |

Criteria for Trained Neural Networks with Appliance in Passive Radiolocation | 191 |

203 | |

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4th Int algorithm analog analysis approximation architecture array assume asymptotic stability autonomous boundary conditions Budapest Budapest Hungary 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 constant continuous functions corresponding defined denotes detection differential equations discrete discrete space eigenvalues equilibrium point Figure FitzHugh-Nagumo equation flux Fuzzy 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 layer Lyapunov function M-matrix matrix method mode neurons node nonlinear nonsingular M-matrix obtained output parameters pattern formation PDEs periodic solutions piecewise linear predicted Proc radiolocation realized Reljin resistor Roska Seville Spain shortest path signal simulation Slavova solving structure Theorem trajectory transform travelling wave solutions Turing Patterns two-dimensional values variables vector voltage Vxij(t wave propagation Workshop CNNA-96 zero