Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Complex Systems Analysis
• Coupled Oscillator Systems

Background:

• Coupled oscillators exhibit diverse synchronization phenomena.
• Amplitude death (AD) is a state where oscillations cease due to coupling.
• Intrinsic time-delays in oscillators can significantly alter system dynamics.

Purpose of the Study:

• To explore and experimentally demonstrate amplitude death (AD) in coupled intrinsic time-delayed hyperchaotic oscillators.
• To identify novel synchronization transition scenarios leading to AD.
• To theoretically and experimentally validate the derived stability conditions for various synchronization states.

Main Methods:

• Theoretical analysis using Krasovskii-Lyapunov theory and linear stability analysis.
• Numerical simulations of coupled hyperchaotic oscillators with mean-field diffusion.
• Experimental validation using an electronic circuit, time-series analysis, phase-plane plots, and generalized autocorrelation functions.

Main Results:

• A novel synchronization transition scenario involving AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS) was identified.
• The transitions are mediated by variations in the difference of intrinsic time-delays.
• For equal intrinsic time-delays, increasing coupling strength leads to a transition from unsynchronized states to AD via CS.

Conclusions:

• The study reveals a new pathway to amplitude death in complex systems driven by intrinsic time-delays.
• The findings provide a theoretical framework and experimental evidence for understanding synchronization transitions in delayed dynamical systems.
• The identified phenomena have potential implications for designing and controlling complex networks.