Bifurcation structure of two Coupled Periodically driven double-well Duffing Oscillators

Abstract

The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force $f$ and its frequency $\Omega$. We first examine the stability of the steady state in linear response, and classify the different types of bifurcation likely to occur in this model. We then explore the complex behaviour associated with these bifurcations numerically. Our results show many striking departures from the behaviour of coupled driven Duffing Oscillators with single well-potentials, as characterised by Kozlowski et al \cite{k1}. In addition to the well known routes to chaos already encountered in a one-dimensional Duffing oscillator, our model exhibits imbricated period-doubling of both types, symmetry-breaking, sudden chaos and a great abundance of Hopf bifurcations, many of which occur more than once for a given driving frequency. We explore the chaotic behaviour of our model using two indicators, namely Lyapunov exponents and the power spectrum. Poincaré cross-sections and phase portraits are also plotted to show the manifestation of coexisting periodic and chaotic attractors including the destruction of $T^2$ tori doubling.

16 pages, 8 figures

References in corpus (2)

• Dynamic Stabilization in The Double-Well Duffing Oscillator
• Symmetry breaking perturbations and strange attractors

Cited by in corpus (5)

• Bifurcation and Chaos in Coupled Ratchets exhibiting Synchronized Dynamics
• Spatio-temporal spread of perturbations in a driven dissipative Duffing chain: an OTOC approach
• Multi-branched resonances, chaos through quasiperiodicity, and asymmetric states in a superconducting dimer
• Patterns and Stability of Coupled Multi-Stable Nonlinear Oscillators
• Nonreciprocal amplification toward chaos in a chain of Duffing oscillators