Related papers: Lyapunov functions for Morse-Smale synchronisation…
We investigate a transition from chaotic to nonchaotic behavior and synchronization in an ensemble of systems driven by identical random forces. We analyze the synchronization phenomenon in the ensemble of particles moving with friction in…
This paper deals with asymptotic stability of a class of dynamical systems in terms of smooth Lyapunov pairs. We point out that well known converse Lyapunov results for differential inclusions cannot be applied to this class of dynamical…
The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system…
We study the collective dynamics of coupled Stuart--Landau oscillators, which model limit-cycle behavior near a Hopf bifurcation and serve as the amplitude-phase analogue of the Kuramoto model. Unlike the well-studied phase-reduced systems,…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
The problem of synchronization and balancing around simple closed polar curves is addressed for unicycle-type multi-agent systems. Leveraging the concept of barrier Lyapunov function in conjunction with bounded Lyapunov-like curve-phase…
We present analytical and numerical results on the joint dynamics of two coupled Duffing oscillators with nonlinearity of opposite signs (hardening and softening). In particular, we focus on the existence and stability of synchronized…
In this paper, we provide a formulation of an open Hegselmann-Krause (HK) dynamics where agents can join and leave the system during the interactions. We consider a stochastic framework where the time instants corresponding to arrivals and…
We study the phenomenon of synchronization in pairs of doubly clamped, mechanically coupled silicon micro-oscillators. A continuous-wave laser beam is used to drive the micro-beams into limit cycle oscillations and to detect the…
We study the long-time dynamics of a bulk-surface convective Cahn--Hilliard system describing phase separation processes with bulk-surface interaction. The presence of convection terms leads to a non-autonomous dynamical system and prevents…
This study explores a method to characterize temporal structure of intermittent phase locking in oscillatory systems. When an oscillatory system is in a weakly synchronized regime away from a synchronization threshold, it spends most of the…
Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling. The linear stability of these states is derived and it…
The emergence of rich dynamical phenomena in coupled self-sustained oscillators, primarily synchronization and amplitude death, has attracted considerable interest in several fields of science and engineering. Here, we present a…
Existence of different kinds of synchronizations, namely anticipatory, complete and lag type synchronizations (both exact and approximate), are shown to be possible in time-delay coupled piecewise linear systems. We deduce stability…
A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators…
Under a high frequency drive, Josephson junctions demonstrate "Shapiro steps" of quantized voltage. These are dynamically stabilized states, in which the phase across the junction locks to the external drive. We explore the stochastic…
We study dynamics of phase-differences (PDs) of coupled oscillators where both the intrinsic frequencies and the couplings vary in time. In case the coupling coefficients are all nonnegative, we prove that the PDs are asymptotically stable…
We investigate the temporal dynamics of the PT-Symmetric nonlinear oscillators in the presence of Duffing nonlinearity for two forms of oscillator configuration. In the former, we consider two oscillator coupled to each other. One…
At arbitrary temperature $T$, we solve for the dynamics of single molecule magnets composed of three classical Heisenberg spins either on a chain with two equal exchange constants $J_1$, or on an isosceles triangle with a third, different…
We study phase-synchronization in a driven two-level system coupled to a non-Markovian bosonic reservoir. The dynamics is described by treating the system-bath coupling and the coherent drive without invoking the rotating-wave…