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World Scientific Series on Nonlinear Science, Series A - Vol. 9
FREQUENCY-DOMAIN METHODS FOR NONLINEAR ANALYSIS: THEORY AND APPLICATIONS
by G A Leonov, D V Ponomarenko & V B Smirnova (St. Petersburg Univ., Russia)
This book deals with the investigation of global attractors of nonlinear dynamical systems. The exposition proceeds from the simplest attractor of a single equilibrium to more complicated ones, i.e. to finite, denumerable and continuum equilibria sets; and further, to cycles, homoclinic and heteroclinic orbits; and finally, to strange attractors consisting of irregular unstable trajectories. On the complicated equilibria sets, the methods of Lyapunov stability theory are transferred. They are combined with stability techniques specially elaborated for such sets. The results are formulated as frequency-domain criteria. The methods connected with the theorems of existence of cycles and homoclinic orbits are developed. The estimates of Hausdorff dimensions of attractors are presented.
Contents:
- Stability of Control Systems with the Unique Equilibrium
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Asymptotic Behavior of Systems with Multiple Equilibria
- Circular Solutions and Cycles
- Existence of Homoclinic Orbits
- Dimension of Attractors
- Bibliography
- Index
Readership: Nonlinear scientists and mathematicians.
| 512pp |
Pub. date: May 1996 |
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