Orbit quantization in a retarded harmonic oscillator
- URL: http://arxiv.org/abs/2301.13608v1
- Date: Wed, 25 Jan 2023 04:47:06 GMT
- Title: Orbit quantization in a retarded harmonic oscillator
- Authors: \'Alvaro G. L\'opez
- Abstract summary: We analytically predict the value of the first Hopf bifurcation, unleashing a self-oscillatory motion.
When the system is driven very far from equilibrium, a multiscale strange attractor displaying intrinsic and robust intermittency is uncovered.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the dynamics of a damped harmonic oscillator in the presence of a
retarded potential with state-dependent time-delayed feedback. In the limit of
small time-delays, we show that the oscillator is equivalent to a Li\'enard
system. This allows us to analytically predict the value of the first Hopf
bifurcation, unleashing a self-oscillatory motion. We compute bifurcation
diagrams for several model parameter values and analyse multistable domains in
detail. Using the Lyapunov energy function, two well-resolved energy levels
represented by two coexisting stable limit cycles are discerned. Further
exploration of the parameter space reveals the existence of a superposition
limit cycle, encompassing two degenerate coexisting limit cycles at the
fundamental energy level. When the system is driven very far from equilibrium,
a multiscale strange attractor displaying intrinsic and robust intermittency is
uncovered.
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