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Gibbs attractor: A chaotic nearly Hamiltonian system, driven by external harmonic force
1Department of Physics, Moscow State University, Moscow 119992, Russia. pve@shg.phys.msu.su
Summary
A perturbed Hamiltonian system can exhibit a Gibbs attractor, similar to canonical distributions. Energy evolution in these chaotic systems demonstrates diffusion-like behavior, studied in a nonlinear oscillator.
Area of Science:
- Nonlinear dynamics
- Statistical mechanics
- Chaos theory
Background:
- Autonomous Hamiltonian systems can exhibit chaotic behavior.
- Perturbations like damping and external forces can alter system dynamics.
- The Gibbs canonical distribution is a fundamental concept in statistical mechanics.
Purpose of the Study:
- To investigate the emergence of Gibbs-like attractors in perturbed chaotic systems.
- To analyze the energy diffusion process in such systems.
- To study the Pullen-Edmonds oscillator's Gibbs attractor properties and parameter dependencies.
Main Methods:
- Analytical investigation of perturbed Hamiltonian systems.
- Numerical simulations of the nonlinear Pullen-Edmonds oscillator.
- Analysis of attractor properties and energy diffusion.
Main Results:
- A strange attractor, termed the Gibbs attractor, can form in perturbed chaotic systems.
- The evolution of energy in these systems resembles diffusion.
- The study characterizes the Gibbs attractor's dependence on perturbation parameters in the Pullen-Edmonds oscillator.
Conclusions:
- Perturbed chaotic Hamiltonian systems can develop Gibbs attractors.
- Energy diffusion is a key characteristic of these systems.
- The Pullen-Edmonds oscillator serves as a model for understanding these phenomena.