No abstract

In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic influence over those dynamics. In many studies, researchers start with a specific model for both the intrinsic dynamics of each agent and the interaction network, and attempt to learn about the dynamics that can be observed in the model. Here we consider the inverse problem: given the dynamics of a system, can one learn about the underlying network? We investigate arbitrary networks of coupled phase-oscillators whose dynamics are characterized by synchronization. We demonstrate that, given sufficient observational data on the transient evolution of each oscillator, one can use machine learning methods to reconstruct the interaction network and simultaneously identify the parameters of a model for the intrinsic dynamics of the oscillators and their coupling.

No abstract

This paper concerns the dynamics of the following nonlinear differential-delay equation:ẋ = −x(t − T ) − x 3 + αx in which T is the delay and α is a coefficient of self-feedback. Using numerical integration, continuation programs and bifurcation theory, we show that this system exhibits a wide range of dynamical phenomena, including Hopf and pitchfork bifurcations, limit cycle folds and relaxation oscillations.

Analytical and numerical methods are applied to a pair of coupled nonidentical phase-only oscillators, where each is driven by the same independent third oscillator. The presence of numerous bifurcation curves defines parameter regions with 2, 4, or 6 solutions corresponding to phase locking. In all cases, only one solution is stable. Elsewhere, phase locking to the driver does not occur, but the average frequencies of the drifting oscillators are in the ratio of m:n. These behaviors are shown analytically to exist in the case of no coupling, and are identified using numerical integration when coupling is included.