Titlebook: An Introduction to Dynamical Systems and Chaos; G. C. Layek Textbook 2024Latest edition The Editor(s) (if applicable) and The Author(s), u

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https://doi.org/10.1007/978-3-662-41370-8sitions represent many natural phenomena or engineering processes. We shall introduce few particular bifurcations, viz., saddle-node (fold), period-doubling (flip), period-bubbling, pitchfork, transcritical bifurcations, and Neimark-Sacker codimension-2 bifurcation in this chapter.

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Stability Theory,quations rigorous mathematical definitions are often too restrictive in analyzing the stability of solutions. We begin with the stability analysis of linear systems. The normal form analysis for stable, unstable and center manifolds, and the center manifold reduction are discussed.

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Symmetry Analysis,ce of symmetry, particularly in analyzing nonlinear systems we devote this chapter on basic idea of group of transformations, Lie group of transformations, Lie group of transformations, some theorems on Lie symmetry, its invariance, Invariance principle and algorithm, and symmetry analysis of some physical systems.

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Continuous Dynamical Systems,eir trajectories cannot be represented by usual geometry. In this chapter we discuss some important definitions, concept of flows, their properties, examples, and analysis of one-dimensional flows for an easy way to understand the nonlinear dynamical systems.

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