Monoj Kumar Sen

Effect of time delay on the onset of synchronization of the stochastic Kuramoto model

We consider the Kuramoto model of globally coupled phase oscillators with time-delayed interactions, that is subject to Ornstein–Uhlenbeck (Gaussian) colored or non-Gaussian colored noise. We investigate numerically the interplay between the influences of the finite correlation time of noise τ and the time delay τd on the onset of the synchronization process. The cases for identical and nonidentical oscillators have both been considered. Among the obtained results for identical oscillators is a large increase of the synchronization threshold as a function of time delay for the colored non-Gaussian noise compared to the case of the colored Gaussian noise at low noise correlation time τ. However, the difference reduces remarkably for large noise correlation times. For the case of nonidentical oscillators, the incoherent state may become unstable around the maximum value of the threshold (as a function of time delay) even at lower coupling strength values in the presence of colored noise as compared to the noiseless case. We have studied the dependence of the critical value of the coupling strength (the threshold of synchronization) on given parameters of the stochastic Kuramoto model in great detail and presented results for possible cases of colored Gaussian and non-Gaussian noises.

Study of non-Markovian dynamics of a charged particle in presence of a magnetic field in a simple way

In this paper, we have investigated the dynamics of a Brownian particle in the presence of a magnetic field. The present investigation is generalized considering different kinds of force fields, magnetic field, and non-Markovian thermal bath. The properties of the Brownian particle have been calculated based on the multi-dimensional Fokker-Planck description of stochastic processes. It leads to the study of non-Markovian dynamics of a Brownian particle in the presence of a magnetic field in a simple way. Using the present simple method, we have identified several important signatures of magnetic field and non-Markovian thermal bath in the dynamics.

Kinetics of self-induced aggregation of Brownian particles : Non-Markovian and non-Gaussian features

In this paper we have explored a model for self-induced aggregation of Brownian particles incorporating non-Markovian and non-Gaussian character of the associated random noise processes. The time evolution of each individual is guided by an overdamped Langevin equation of motion with a nonlocal drift arising out of the imbalance in the local distribution of the other individuals. Our simulation results show that colored noise enhances the tendency of cluster formation. Another observation is that the critical noise variance decreases at first with increase in noise correlation time followed by an increase after exhibiting a minimum. Furthermore, in the long time limit the cluster number in the aggregation process exhibits depletion with time following a power law with an exponent which increases remarkably with non-Markovian character of the noise processes.

Noise induced escape through an unstable limit cycle in the presence of a fluctuating barrier

The escape of Brownian particles through an unstable limit cycle in the presence of deterministic barrier fluctuations has been studied. It has been observed that with increasing non-Gaussian character of the noise, resonant activation gets suppressed and periodically forced resonant activation becomes robust. Secondly, the ratio of the mean lifetimes in the presence and in the absence of barrier fluctuation increases very rapidly with the damping constant for Gaussian noise unlike that for the non-Gaussian case. This ratio decreases sharply for deviation of the noise behavior from Gaussian characteristics. The Arrhenius plot, on the other hand, exhibits deviation from linearity particularly at large noise strength for both Gaussian and non-Gaussian cases. The deviation is large for non-Gaussian noise. We have also shown that additive colored non-Gaussian noise can induce RA-like phenomena even in a system having harmonic potential energy.

Synchronization of Nonidentical Coupled Phase Oscillators in the Presence of Time Delay and Noise

We have studied in this paper the dynamics of globally coupled phase oscillators having the Lorentzian frequency distribution with zero mean in the presence of both time delay and noise. Noise may be Gaussian or non-Gaussian in characteristics. In the limit of zero noise strength, we find that the critical coupling strength (CCS) increases linearly as a function of time delay. Thus the role of time delay in the dynamics for the deterministic system is qualitatively equivalent to the effect of frequency fluctuations of the phase oscillators by additive white noise in absence of time delay. But for the stochastic model, the critical coupling strength grows nonlinearly with the increase of the time delay. The linear dependence of the critical coupling strength on the noise intensity also changes to become nonlinear due to creation of additional phase difference among the oscillators by the time delay. We find that the creation of phase difference plays an important role in the dynamics of the system when the intrinsic correlation induced by the finite correlation time of the noise is small. We also find that the critical coupling is higher for the non-Gaussian noise compared to the Gaussian one due to higher effective noise strength.

Study of Thermodynamically Inspired Quantities for Both Thermaland External Colored Non-Gaussian Noises Driven Dynamical System

We have studied dynamics of both internal and external noises-driven dynamical system in terms of information entropy at both nonstationary and stationary states. Here a unified description of entropy flux and entropy production is considered. Based on the Fokker-Planck description of stochastic processes and the entropy balance equation we have calculated time dependence of the information entropy production and entropy flux in presence and absence of nonequilibrium constraint (NEC). In the presence of NEC we have observed extremum behavior in the variation of entropy production as function of damping strength, noise correlation, and non-Gaussian parameter (which determine the deviation of external noise behavior from Gaussian characteristic), respectively. Thus the properties of noise process are important for entropy production.

THE EFFECT OF INTERFERENCE IN ADDITIVE AND MULTIPLICATIVE WHITE NOISES ON INFORMATION ENTROPY PRODUCTION AND ENTROPY FLUX

In this paper we study time evolution of configuration space in terms of information entropy flux and entropy production for colored cross-correlated noise-driven open systems. The effect of interference in additive and multiplicative white noises on entropy flux and entropy production is calculated based on the Fokker–Planck description of the stochastic process and information entropy balance equation. The variation of entropy production with the damping constant or strength of multiplicative noise reveals nonmonotonic behavior as a result of the interplay of deterministic and random forces.