Appearance of chaos and hyperchaos in evolving pendulum network
Vyacheslav O Munyaev1, Dmitry S Khorkin1, Maxim I Bolotov1
1Department of Control Theory, Scientific and Educational Mathematical Center "Mathematics of Future Technologies," Nizhny Novgorod State University, Gagarin Ave. 23, Nizhny Novgorod 603950, Russia.
Chaos (Woodbury, N.Y.)
|July 9, 2021
Summary
Deterministic chaos emerges in coupled pendulums through dissipation or changes in ensemble size. Chaos arises hard with discrete parameter changes, and coupling strength influences its occurrence.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Chaos theory
Background:
- Deterministic chaos is a key area in nonlinear dynamics.
- Research spans low-dimensional systems to coupled oscillators.
- Understanding chaos emergence in ensembles is crucial.
Purpose of the Study:
- Investigate chaos emergence in locally coupled pendulums with constant torque.
- Analyze how dissipation, ensemble size, and coupling strength affect chaos.
- Characterize bifurcation scenarios and chaotic properties.
Main Methods:
- Analysis of period-doubling and invariant tori destruction bifurcations.
- Numerical experiments to confirm analytical findings.
- Examination of discrete parameter changes (ensemble size) and continuous parameters (dissipation, coupling).
Main Results:
- Increased dissipation can induce chaos via bifurcations.
- Adding/excluding elements triggers hard-emerging chaos/hyperchaos.
- Chaos appears with weak/moderate coupling due to mode overlap; absent with strong coupling.
- Hyperchaos dimension depends on the number of elements.
Conclusions:
- Dissipation and ensemble size are critical factors for chaos in pendulum chains.
- Coupling strength exhibits a specific, non-monotonic influence on chaos.
- The study provides analytical and numerical insights into complex dynamics.
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