Generalizing the transition from amplitude to oscillation death in coupled oscillators

Area of Science:

• Nonlinear dynamics
• Complex systems
• Coupled oscillators

Background:

• Amplitude death (AD) and oscillation death (OD) are distinct phenomena that quench oscillations in coupled nonlinear systems.
• Previous work demonstrated AD-to-OD transitions driven by heterogeneity and coupling strength.

Purpose of the Study:

• To investigate the AD-to-OD transition in nonlinear oscillators with diverse coupling mechanisms.
• To explore the role of time delays and specific coupling types in facilitating this transition.

Main Methods:

• Analysis of coupled nonlinear oscillators with varying coupling natures, including time-delayed, dynamic, and conjugate couplings.
• Examination of system behavior under conditions of oscillator heterogeneity and identity.

Main Results:

• Time delays do not induce AD-to-OD transitions in identical oscillators but facilitate them with heterogeneity.
• Dynamic and conjugate couplings reliably induce the AD-to-OD transition even in identical oscillators.
• The study reveals the coexistence of AD and OD, along with diverse stable OD states post-transition.

Conclusions:

• The findings expand the understanding of oscillation quenching mechanisms in coupled systems.
• The identified transition pathways and resulting states have implications for physics, biology, and control engineering.