Asymmetry in initial cluster size favors symmetry in a network of oscillators.

Counterintuitive to the common notion of symmetry breaking, asymmetry favors synchrony in a network of oscillators. Our observations on an ensemble of identical Stuart-Landau systems under a symmetry breaking coupling support our conjecture. As usual, for a complete deterministic and the symmetric choice of initial clusters, a variety of asymptotic states, namely, multicluster oscillation death (1-OD, 3-OD, and m -OD), chimera states, and traveling waves emerge. Alternatively, multiple chimera death (1-CD, 3-CD, and m -CD) and completely synchronous states emerge in the network whenever some randomness is added to the symmetric initial states. However, in both the cases, an increasing asymmetry in the initial cluster size restores symmetry in the network, leading to the most favorable complete synchronization state for a broad range of coupling parameters. We are able to reduce the network model using the mean-field approximation that reproduces the dynamical features of the original network.

Manipulating localized matter waves in multicomponent Bose-Einstein condensates.

We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameters and external trap potentials through a similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schrödinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures; namely, rogue waves, dark- and bright-soliton rogue waves, and rogue-wave breatherlike structures for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Furthermore, we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for the repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single-, two-, and three-composite rogue waves for three-component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials.

Manipulating matter rogue waves and breathers in Bose-Einstein condensates.

We construct higher-order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps: (i) the time-independent expulsive trap, (ii) time-dependent monotonous trap, and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second- and third-order rogue waves transform into the first-order-like rogue waves. We also analyze the density profiles of breather solutions. Here we also show that the shapes of the breathers change when we tune the strength of the trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.

Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators.

Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at (mN(c)+1)-th oscillators in the ring, where m is an integer and N(c) is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by size instability. We also demonstrate that there exists an exponential relation between the number of oscillators that can support stable synchronization in the ring with the external drive and the critical coupling strength ε(c) with a scaling exponent γ. The critical coupling strength is calculated by numerically estimating the synchronization error and is also confirmed from the conditional Lyapunov exponents of the coupled systems. We find that the same scaling relation exists for m couplings between the drive and the ring. Further, we have examined the robustness of the synchronous states against Gaussian white noise and found that the synchronization error exhibits a power-law decay as a function of the noise intensity indicating the existence of both noise-enhanced and noise-induced synchronizations depending on the value of the coupling strength ε. In addition, we have found that ε(c) shows an exponential decay as a function of the number of additional couplings. These results are demonstrated using the paradigmatic models of Rössler and Lorenz oscillators.

Desynchronized wave patterns in synchronized chaotic regions of coupled map lattices.

We analyze the size limits of coupled map lattices with diffusive coupling at the crossover of low-dimensional to high-dimensional chaos. We investigate the existence of standing-wave-type periodic patterns, within the low-dimensional limit, in addition to the stable synchronous chaotic states depending upon the initial conditions. Further, we bring out a controlling mechanism to explain the emergence of standing-wave patterns in the coupled map lattices. Finally, we give an analytic expression in terms of the unstable periodic orbits of the isolated map to represent the standing-wave patterns.

Bifurcation analysis of the travelling waveform of FitzHugh-Nagumo nerve conduction model equation.

The FitzHugh-Nagumo model for travelling wave type neuron excitation is studied in detail. Carrying out a linear stability analysis near the equilibrium point, we bring out various interesting bifurcations which the system admits when a specific Z(2) symmetry is present and when it is not. Based on a center manifold reduction and normal form analysis, the Hopf normal form is deduced. The condition for the onset of limit cycle oscillations is found to agree well with the numerical results. We further demonstrate numerically that the system admits a period doubling route to chaos both in the presence as well as in the absence of constant external stimuli. (c) 1997 American Institute of Physics.