Explosive transitions in coupled Lorenz oscillators.

We study the transition to synchronization in an ensemble of chaotic oscillators that are interacting on a star network. These oscillators possess an invariant symmetry and we study emergent behavior by introducing the timescale variations in the dynamics of the nodes and the hub. If the coupling preserves the symmetry, the ensemble exhibits consecutive explosive transitions, each one associated with a hysteresis.

Collective dynamics of coupled Lorenz oscillators near the Hopf boundary: Intermittency and chimera states.

We study collective dynamics of networks of mutually coupled identical Lorenz oscillators near a subcritical Hopf bifurcation. Such systems exhibit induced multistable behavior with interesting spatiotemporal dynamics including synchronization, desynchronization, and chimera states. For analysis, we first consider a ring topology with nearest-neighbor coupling and find that the system may exhibit intermittent behavior due to the complex basin structures and dynamical frustration, where temporal dynamics of the oscillators in the ensemble switches between different attractors.

Finite-size scaling of critical avalanches.

We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it may also decrease with increasing the system size at a fixed avalanche size. We implement the scaling method and identify scaling functions.

Controlling chimera states in chaotic oscillator ensembles through linear augmentation.

In this work, we show how "chimera states," namely, the dynamical situation when synchronized and desynchronized domains coexist in an oscillator ensemble, can be controlled through a linear augmentation (LA) technique. Specifically, in the networks of coupled chaotic oscillators, we obtain chimera states through induced multistability and demonstrate how LA can be used to control the size and spatial location of the incoherent and coherent populations in the ensemble. We examine basins of attraction of the system to analyze the effects of LA on its multistable behavior and thus on chimera states.

Generalized synchrony of coupled stochastic processes with multiplicative noise.

We study the effect of multiplicative noise in dynamical flows arising from the coupling of stochastic processes with intrinsic noise. Situations wherein such systems arise naturally are in chemical or biological oscillators that are coupled to each other in a drive-response configuration. Above a coupling threshold we find that there is a strong correlation between the drive and the response: This is a stochastic analog of the phenomenon of generalised synchronization.

Nature of weak generalized synchronization in chaotically driven maps.

Weak generalized synchrony in a drive-response system occurs when the response dynamics is a unique but nondifferentiable function of the drive, in a manner that is similar to the formation of strange nonchaotic attractors in quasiperiodically driven dynamical systems. We consider a chaotically driven monotone map and examine the geometry of the limit set formed in the regime of weak generalized synchronization. The fractal dimension of the set of zeros is studied both analytically and numerically.

Phantom instabilities in adiabatically driven systems: dynamical sensitivity to computational precision.

We study the robustness of dynamical phenomena in adiabatically driven nonlinear mappings with skew-product structure. Deviations from true orbits are observed when computations are performed with inadequate numerical precision for monotone, periodic, or quasiperiodic driving. The effect of slow modulation is to "freeze" orbits in long intervals of purely contracting or purely expanding dynamics in the phase space.

Transition to weak generalized synchrony in chaotically driven flows.

We study regimes of strong and weak generalized synchronization in chaotically forced nonlinear flows. The transition between these dynamical states can occur via a number of different routes, and here we examine the onset of weak generalized synchrony through intermittency and blowout bifurcations. The quantitative characterization of this dynamical transition is facilitated by measures that have been developed for the study of strange nonchaotic motion.