%0 Journal Article %1 Saxena2012205 %A Saxena, Garima %A Prasad, Awadhesh %A Ramaswamy, Ram %D 2012 %J Physics Reports %K ODEs analysis chaos classical mathematics mechanics physics qualitative review theory %N 5 %P 205 - 228 %R 10.1016/j.physrep.2012.09.003 %T Amplitude death: The emergence of stationarity in coupled nonlinear systems %U http://www.sciencedirect.com/science/article/pii/S0370157312002645 %V 521 %X 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.

@article{Saxena2012205, abstract = {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.}, added-at = {2012-11-29T16:43:16.000+0100}, author = {Saxena, Garima and Prasad, Awadhesh and Ramaswamy, Ram}, biburl = {https://www.bibsonomy.org/bibtex/292c9a521dcea8743dcb9347209c5fbf5/drmatusek}, doi = {10.1016/j.physrep.2012.09.003}, interhash = {c37b44d80fc60f77d06d8eb1c6abf6b5}, intrahash = {92c9a521dcea8743dcb9347209c5fbf5}, issn = {0370-1573}, journal = {Physics Reports}, keywords = {ODEs analysis chaos classical mathematics mechanics physics qualitative review theory}, month = dec, number = 5, pages = {205 - 228}, timestamp = {2014-01-11T04:19:11.000+0100}, title = {Amplitude death: The emergence of stationarity in coupled nonlinear systems}, url = {http://www.sciencedirect.com/science/article/pii/S0370157312002645}, volume = 521, year = 2012 }