An Introduction to Dynamical Systems and Chaos

This book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, hyperchaos, Shil'nikov chaos, quantifying chaos, routes to chaos and multistable coexisting attractors. A systematic mathematical approach has been adopted, and several examples are worked out in details and exercises have been included. The book is useful for courses in dynamical systems and chaos theory.The bifurcation theories for both continuous and discrete systems are presented thoroughly with physical examples.The conjugacy and circle homeomorphism are included.The organized structures in bi-parameter plane for transitional and chaotic regimes are now active research interest and discussed elaborately. The connections of complex chaotic attractors with fractal cascading are explored in many physical systems. Chaotic attractors may attain multiple scaling factors and show scale invariance property. The idea of multifractals and global spectrum for quantifying inhomogeneous chaotic attractors are discussed.