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Amplitude death phenomena in delay-coupled Hamiltonian systems
Garima Saxena1, Awadhesh Prasad, Ram Ramaswamy
1Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.
Summary
Coupling Hamiltonian systems with time delays can lead to amplitude death (AD), where oscillations cease and point attractors stabilize. This phenomenon, observed in harmonic and anharmonic oscillators, involves transient phase flips.
Area of Science:
- Nonlinear Dynamics and Chaos Theory
- Theoretical Physics
- Coupled Oscillator Systems
Background:
- Uncoupled Hamiltonian systems exhibit periodic, quasiperiodic, or chaotic motion.
- Time-delayed interactions in coupled systems fundamentally alter system dynamics.
- Conservation laws are violated in Hamiltonian systems with delay coupling.
Purpose of the Study:
- To investigate the emergence of attractors in Hamiltonian systems coupled via time delays.
- To analyze the phenomenon of amplitude death (AD) in such systems.
- To explore the transient dynamics, including phase flips, during the approach to AD.
Main Methods:
- Theoretical analysis of coupled Hamiltonian systems with time-delayed interactions.
- Numerical simulations and phase space analysis to identify attractors.
- Application to specific models: harmonic oscillators and the Hénon-Heiles system.
Main Results:
- Time-delayed coupling can create attractors in the phase space, deviating from conservative behavior.
- Sufficiently strong coupling leads to amplitude death (AD), characterized by stabilized point attractors and cessation of oscillations.
- Transient dynamics show a distinct phase flip phenomenon as the system approaches AD.
Conclusions:
- Time-delayed coupling introduces non-conservative behavior and novel dynamical states in Hamiltonian systems.
- Amplitude death is a significant emergent phenomenon in these coupled systems.
- The study provides insights into the complex dynamics of delayed coupled oscillators, including the Hénon-Heiles system.
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