Amplitude death: The emergence of stationarity in coupled nonlinear systems

By Garima Saxena, Awadhesh Prasad, R. Ramaswamy. 2012

332 citations recorded by the source corpus.

When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points which the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behavior is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d8d877dac43c1f8272945395fd0da899e304ee97

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Hidden attractors in dynamical systems (2016, background): “One of the important schemes for the stabilization of the fixed point can be done by using the phenomenon of amplitude or oscillation death [168, 169] due to interactions between the coupled oscillators.”
Coupling functions:universal insights into dynamical interaction mechanisms (2017, background): “…et al., 2005; Kapitaniak et al., 2012; Lehnertz and Elger, 1998; Pikovsky et al., 2001), oscillation and amplitude death (Koseska et al., 2013a; Saxena et al., 2012), birth of oscillations (Pogromsky et al., 1999; Smale, 1976), breathers (MacKay and Aubry, 1994), coexisting phases (Keller et…”
Oscillation quenching mechanisms: Amplitude vs. oscillation death (2013, background): “In what follows, we discuss very briefly the most common mechanisms that lead to AD; for a more extensive discussion on AD manifestation and control we refer the reader to [51].”
Synchronization in complex networks and its application - A survey of recent advances and challenges (2014, background): “…of control-oriented investigations (actually within the scope of statistical physics and nonlinear physics) and some reviews on oscillation death or amplitude death of complex networks have been reported (Koseska et al., 2013; Saxena et al., 2012), the state of art on them will not be pursued here.”