The Analysis Of Coupled Oscillatory Systems Essays

2057 Words Sep 15th, 2016 9 Pages
The analysis of coupled oscillatory systems is an important research field bridging between nonlinear dynamics, network science, and statistical physics, with a variety of applications in physics, biology, and technology.3,4 The study of large networks with complex coupling schemes continues to open up new unexpected dynamical scenarios. One of them is chimera states, which have been intensively studied in the networks of phase oscillators5–14 and in a variety of different systems including neural systems,15–17 population dynamics,18 nonlinear oscillators,19–21 and quantum oscillator systems.22 The intriguing chimera states have been observed in higher spatial dimensions,8,12,23–27 and recent studies uncover new types of chimeras having multiple incoherent regions,15,21,28–30 as well as amplitude-mediated,31,32 and pure amplitude chimera and chimera death states.33
While pioneering studies have focused mostly on the nonlocally coupled and two-subpopulations topologies, also global all-to-all coupling,32,34–36 and even more complex coupling topologies allow for the existence of chimera states.17,18,37–42 Furthermore, a new type of alternating chimera states has been observed.43,44 Chimera states have also been shown to be robust against inhomogeneities of the local dynamics and coupling topology,42,45–47 as well as against noise,48 or they might even be induced by noise.49,50
The study of chimera states can be useful in natural and technological systems,…

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