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Multistability in the Duffing--Holmes oscillator: basins of antiperiodic, periodic, and chaotic attractors and their relative volumes
Arturo C. Marti, Edson D. Leonel
The periodically driven Duffing--Holmes oscillator is strongly multistable: for the same forcing amplitude and frequency, periodic, chaotic, and antiperiodic attractors coexist, ea…
Recurrence and anti-recurrence patterns reveal an antiperiodic fingerprint that survives into chaos in the Duffing--Holmes oscillator
Arturo C. Marti, Edson D. Leonel
The periodically forced Duffing--Holmes oscillator possesses a discrete symmetry under sign reversal of the coordinate combined with a half-period shift of the drive. When this sym…
Antiperiodicity in the Duffing--Holmes oscillator: symmetry origin, parity selection, and transitions
Arturo C. Marti, Edson D. Leonel
We investigate the origin and distribution of antiperiodicity --- oscillations satisfying --- in the periodically driven Duffing--Holmes oscillator, combining analyt…
Experimental observation of chaotic and multistable dynamics in a Duffing--Holmes--type analog circuit: antiperiodicity and attractor-coexistence signatures
Patricia R. Gargiulo, Caracé Gutiérrez, Juan P. Tarigo +2
An experimental study of a periodically forced Duffing--Holmes-type oscillator with a double-well potential, emulated by a piecewise-linear analog electronic circuit, is presented.…
Phase-space organization of the elastic pendulum: chaotic fraction, energy exchanges, and the order-chaos-order transition
Juan P. Tarigo, Cecilia Stari, Edson D. Leonel +1
We study the phase-space organization of the planar elastic pendulum as a function of its two dimensionless control parameters: the reduced energy and the squared frequency rat…
Describing a Universal Critical Behavior in a transition from order to chaos
Edson D. Leonel, Mayla A. M. de Almeida, Juan Pedro Tarigo +2
We present a comprehensive discussion of a transition from integrability to non-integrability in an oval billiard with a static boundary. This transition is controlled by a deforma…
Universal Second-Order Phase Transition from Integrability to Chaos
Edson D. Leonel, Mayla A. M. de Almeida, Juan Pedro Tarigo +2
We report a dynamical phase transition from integrability to non-integrability in a simple oval-like billiard with boundary . For , the phase space is {\it f…
Regular and chaotic phase space fraction in the double pendulum
Santiago Cabrera, Edson D. Leonel, Arturo C. Marti
The double coplanar pendulum is an example of the coexistence of regular and chaotic dynamics for equal energy values but different initial conditions. Regular trajectories predomi…