Chaotic Dynamics in a Class of Switched Li\'{e}nard/Rayleigh Systems with Relativistic Acceleration

Duccio Papini, Gabriele Villari, Fabio Zanolin


We consider a class of time-periodic switched systems, which
are obtained as a perturbation of a planar autonomous reversible system
by a periodic forcing term.
The model is motivated by an extension of the classical Li\'{e}nard and Rayleigh
equations due to the presence of a relativistic acceleration.
Using recent results from the theory of topological horseshoes,
we provide a new result of existence of infinitely many subharmonic
solutions, as well as more complex dynamics, as illustrated by some numerical examples.


Reversible systems; Quadratic Li\'{e}nard equations; Rayleigh equations; Relativistic acceleration; Switched systems; Periodic solutions; Complex dynamics

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