Toward Analytical Chaos in Nonlinear Systems (PDF)

Exact analytical solutions to periodic motions in nonlinear
dynamical systems are almost not possible. Since the 18th century,
one has extensively used techniques such as perturbation methods to
obtain approximate analytical solutions of periodic motions in
nonlinear systems. However, the perturbation methods cannot provide
the enough accuracy of analytical solutions of periodic motions in
nonlinear dynamical systems. So the bifurcation trees of periodic
motions to chaos cannot be achieved analytically. The author
has developed an analytical technique that is more effective to
achieve periodic motions and corresponding bifurcation trees to
chaos analytically.

Toward Analytical Chaos in Nonlinear Systems
systematically presents a new approach to analytically determine
periodic flows to chaos or quasi-periodic flows in nonlinear
dynamical systems with/without time-delay. It covers the
mathematical theory and includes two examples of nonlinear systems
with/without time-delay in engineering and physics. From the
analytical solutions, the routes from periodic motions to chaos are
developed analytically rather than the incomplete numerical routes
to chaos. The analytical techniques presented will provide a
better understanding of regularity and complexity of periodic
motions and chaos in nonlinear dynamical systems.

Key features:

* Presents the mathematical theory of analytical solutions of
periodic flows to chaos or quasieriodic flows in nonlinear
dynamical systems

* Covers nonlinear dynamical systems and nonlinear vibration
systems

* Presents accurate, analytical solutions of stable and unstable
periodic flows for popular nonlinear systems

* Includes two complete sample systems

* Discusses time-delayed, nonlinear systems and time-delayed,
nonlinear vibrational systems

* Includes real world examples

Toward Analytical Chaos in Nonlinear Systems is a
comprehensive reference for researchers and practitioners across
engineering, mathematics and physics disciplines, and is also a
useful source of information for graduate and senior undergraduate
students in these areas.