The results described in the book have both inter- and transdisciplinary features and are of fundamental importance in nonlinear science

1. Introduction: Synergetics and Models of Continuous and Discrete Active Media. Steady States and Basic Motions (Waves, Dissipative Solitons, etc.).- 1.1 Basic Concepts, Phenomena and Context.- 1.2 Continuous Models.- 1.3 Chain and Lattice Models with Continuous Time.- 1.4 Chain and Lattice Models with Discrete Time.- 2. Solitary Waves, Bound Soliton States and Chaotic Soliton Trains in a Dissipative Boussinesq-Korteweg-de Vries Equation.- 2.1 Introduction and Motivation.- 2.2 Model Equation.- 2.3 Traveling Waves.- 2.4 Homoclinic Orbits. Phase-Space Analysis.- 2.5 Multiloop Homoclinic Orbits and Soliton-Bound States.- 2.6 Further Numerical Results and Computer Experiments.- 2.7 Salient Features of Dissipative Solitons.- 3. Self-Organization in a Long Josephson Junction.- 3.1 Introduction and Motivation.- 3.2 The Perturbed Sine-Gordon Equation.- 3.3 Bifurcation Diagram of Homoclinic Trajectories.- 3.4 Current-Voltage Characteristics of Long Josephson Junctions 54.- 3.5 Bifurcation Diagram in the Neighborhood of c = 1.- 3.6 Existence of Homoclinic Orbits.- 3.7 Salient Features of the Perturbed Sine-Gordon Equation.- 4. Spatial Structures, Wave Fronts, Periodic Waves, Pulses and Solitary Waves in a One-Dimensional Array of Chua's Circuits.- 4.1 Introduction and Motivation.- 4.2 Spatio-Temporal Dynamics of an Array of Resistively Coupled Units.- 4.3 Spatio-Temporal Dynamics of Arrays with Inductively Coupled Units.- 4.4 Chaotic Attractors and Waves in a One-Dimensional Array of Modified Chua's Circuits.- 4.5 Salient Features of Chua's Circuit in a Lattice.- 5. Patterns, Spatial Disorder and Waves in a Dynamical Lattice of Bistable Units.- 5.1 Introduction and Motivation.- 5.2 Spatial Disorder in a Linear Chain of Coupled Bistable Units.- 5.3 Clustering and PhaseResetting in a Chain of Bistable Nonisochronous Oscillators.- 5.4 Clusters in an Assembly of Globally Coupled Bistable Oscillators.- 5.5 Spatial Disorder and Waves in a Circular Chain of Bistable Units.- 5.6 Chaotic and Regular Patterns in Two-Dimensional Lattices of Coupled Bistable Units.- 5.7 Patterns and Spiral Waves in a Lattice of Excitable Units.- 5.8 Salient Features of Networks of Bistable Units.- 6. Mutual Synchronization, Control and Replication of Patterns and Waves in Coupled Lattices Composed of Bistable Units.- 6.1 Introduction and Motivation.- 6.2 Layered Lattice System and Mutual Synchronization of Two Lattices.- 6.3 Controlled Patterns and Replication of Form.- 6.4 Salient Features of Replication Processes via Synchronization of Patterns and Waves with Interacting Bistable Units.- 7. Spatio-Temporal Chaos in Bistable Coupled Map Lattices.- 7.1 Introduction and Motivation.- 7.2 Spectrum of the Linearized Operator.- 7.3 Spatial Chaos in a Discrete Version of the One-Dimensional FitzHugh-Nagumo-Schlögl Equation.- 7.4 Chaotic Traveling Waves in a One-Dimensional Discrete FitzHugh-Nagumo-Schlögl Equation.- 7.5 Two-Dimensional Spatial Chaos.- 7.6 Synchronization in Two-Layer Bistable Coupled Map Lattices.- 7.7 Instability of the Synchronization Manifold.- 7.8 Salient Features of Coupled Map Lattices.- 8. Conclusions and Perspective.- Appendices.- A. Integral Manifolds of Stationary Points.- D. Instability of Spatially Homogeneous States.- E. Topological Entropy and Lyapunov Exponent.- F. Multipliers of the Fixed Point of the Coupled Map Lattice (7.55).- G. Gershgorin Theorem.- References.