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This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB® software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze more complicated models from modern engineering, ecology, and economics.

Cartography --- Bifurcation theory. --- Mathematical models.

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Mathematical physics --- Bifurcation theory --- Congresses. --- Congresses --- Bifurcation theory - Congresses --- Mathematical physics - Congresses --- Bifurcation (not cas) --- Physics

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Bifurcation theory --- Catastrophes (Mathematics) --- Differentiable dynamical systems --- Bifurcation, Théorie de la --- Catastrophes, Théorie des --- Systèmes dynamiques --- Bifurcation, Théorie de la. --- Catastrophes, Théorie des. --- Systèmes dynamiques. --- Bifurcation, Théorie de la. --- Catastrophes, Théorie des. --- Systèmes dynamiques.

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"This book covers solid mechanics for non-linear elastic and elastoplastic materials, describing the behaviour of ductile material subject to extreme mechanical loading and its eventual failure. The book highlights constitutive features to describe the behaviour of frictional materials such as geological media. On the basis of this theory, including large strain and inelastic behaviours, bifurcation and instability are developed with a special focus on the modelling of the emergence of local instabilities such as shear band formation and flutter of a continuum. The former is regarded as a precursor of fracture, while the latter is typical of granular materials. The treatment is complemented with qualitative experiments, illustrations from everyday life and simple examples taken from structural mechanics"

Nonlinear mechanics. --- Materials --- Elastic analysis (Engineering) --- Bifurcation theory. --- Mechanical properties.

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By providing an introduction to nonlinear differential equations, Dr Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincaré-Bendixson theorem, the Hopf bifurcation and chaotic systems. The unique treatment that is found in this book will prove to be an essential guide to stability and chaos.

Differential equations, Nonlinear. --- Bifurcation theory. --- Chaotic behavior in systems.