Planar Pseudo-almost Limit Cycles and Applications to solitary Waves
- Bourama Toni btoni@vsu.edu
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DOI:
https://doi.org/10.4067/S0719-06462013000100009Abstract
We investigate the existence of pseudo-almost limit cycles, a new class of non-periodicity at the interface of the theories of limit cycles and pseudo-almost periodicity. We determine the conditions of existence for several systems including some pseudo-almost periodic perturbations of the harmonic oscillator and the renowned Li´enard systems. We apply to derive the existence of pseudo-almost periodic solitary waves by perturbing first then transforming some hyperbolic and parabolic partial differential equations to Li´enard-type equations. Included also are open questions on the co-existence of limit cycles and strictly pseudo-almost periodic limit cycles partitioning the phase space, and the existence of isochronous pseudo-almost limit cycles.