by V S Afraimovich , V I Nekorkin , G V Osipov , & V D Shalfeev

The understanding of fields and media using discrete lattice models has been greatly aided by the advent of powerful computers. This has also led to the formulation of new and inspiring problems associated with the analysis of homogeneous discrete networks of interacting dynamical elements. This book investigates the nonlinear dynamics of peculiar discrete media made up of interconnected phase synchronization systems. After an introduction which sets out the nature of the problem, the book goes on to consider dynamic processes in chain and lattice networks, utilising both continuous and discrete synchronization systems as component elements. Computational studies aimed at oscillatory-wave phenomena will make the book valuable for specialists in radio engineering, biological excitable media and other branches of physics and biology as well as specialists in applied mathematics and nonlinear sciences.

• Basic Models, Dynamics of a Chain of Phase Lock-Loop Systems with Unidirectional Coupling
• Effect of Inertia of Elements on the Dynamics of a Flow Chain
• Chains with Mutual Coupling
• Chains with Coupling through Phase Mismatching Signals
• Nonlinear Dynamics of Lattices
• Analysis of Stationary Synchronization Regimes
• Some Remarks on Other Kinds of Chains of Synchronization Systems
• Stability and Chaos in the Chains of Discrete Phase-Lock Loops
• Dynamics of a Ring Chain of Discrete Systems
• Order and Chaos in the Discrete Model of an Active Medium
• Results and Problems