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This book examines discrete dynamical systems with memory-nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems.
The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.

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Memorized Linear Discrete Systems.- Memorized Nonlinear Discrete Systems.- Discretization of Time-delay Systems.- Periodic Flows in Time-delay Systems.- Time-delay Duffing Oscillator.

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"This monograph is devoted to the study of discrete dynamical systems with memory. It gives a comprehensive presentation of methods that have been developed for time-delay systems which can be discretized into the memorized discrete dynamical systems." (Anatoly Martynyuk, zbMATH 1408.93001, 2019)

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Professor Albert C.J. Luo is Professor of Mechanical Engineering at the University of Southern Illinois, Edwardsville.

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