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Analytical conditions for the existence of a two-parameter family of periodic orbits in nonautonomous dynamical systems

✍ Scribed by Jan Awrejcewicz; Tsuneo Someya

Publisher
Springer Netherlands
Year
1993
Tongue
English
Weight
486 KB
Volume
4
Category
Article
ISSN
0924-090X

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✦ Synopsis

The two-parameter perturbation method, applied to the example of periodic oscillations in periodically driven mmlinear dynamical systems, is presented. The analytical conditions are given for the existence of a two-parameter family of periodic orbits in nonautonomous dynamical systems in both non-resonance and resonance cases.

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The necessary and sufficient conditions
The necessary and sufficient conditions for the existence of periodic orbits in a Lotka–Volterra system
✍ Yuanshi Wang πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 137 KB

By extending Darboux method to three dimension, we present necessary and sufficient conditions for the existence of periodic orbits in three species Lotka-Volterra systems with the same intrinsic growth rates. Therefore, all the published sufficient or necessary conditions for the existence of perio