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Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data
Jaideep Pathak, Zhixin Lu, Brian R. Hunt +2
We use recent advances in the machine learning area known as 'reservoir computing' to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic…
Modeling the Network Dynamics of Pulse-Coupled Neurons
Sarthak Chandra, David Hathcock, Kimberly Crain +3
We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distrib…
Dynamical Transitions in Large Systems of Mean Field-Coupled Landau-Stuart Oscillators: Extensive Chaos and Clumped States
Wai Lim Ku, Michelle Girvan, Edward Ott
In this paper, we study dynamical systems in which a large number of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed…
Multiscale Dynamics in Communities of Phase Oscillators
Dustin Anderson, Ari Tenzer, Gilad Barlev +3
We investigate the dynamics of systems of many coupled phase oscillators with het- erogeneous frequencies. We suppose that the oscillators occur in M groups. Each oscillator is con…
Echo Phenomena in Large Systems of Coupled Oscillators
Edward Ott, John H. Platig, Thomas M. Antonsen +1
As exemplified by the Kuramoto model, large systems of coupled oscillators may undergo a transition to phase coherence with increasing coupling strength. It is shown that below the…
External Periodic Driving of Large Systems of Globally Coupled Phase Oscillators
T. M. Antonsen, R. T. Faghih, M. Girvan +2
Large systems of coupled oscillators subjected to a periodic external drive occur in many situations in physics and biology. Here the simple, paradigmatic case of equal-strength, a…