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.

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.

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In this paper we have investigated the effect of a magnetic field on the barrier crossing rate of a charged particle. At the low friction regime we have observed a new turnover phenomenon for the variation of rate as a function of field strength. Thus although the force due to the magnetic field is not dissipative in nature, it plays a role in the steady state barrier crossing rate similar to that of a dissipative force in the weak damping regime. For appreciable damping strength, the rate monotonically decreases with the increase of field strength. We have demonstrated an interesting resonance effect due to the variation of frequency of the harmonic oscillator associated with the y-component motion at low damping and magnetic field strength.

In this paper we have calculated escape rate from a meta stable state in the presence of both colored internal thermal and external nonthermal noises. For the internal noise we have considered usual gaussian distribution but the external noise may be gaussian or non-gaussian in characteristic. The calculated rate is valid for low noise strength of non-gaussian noise such that an effective gaussian approximation of non-gaussian noise wherein the higher order even cumulants of order "4" and higher are neglected. The rate expression we derived here reduces to the known results of the literature, as well as for purely external noise driven activated rate process. The latter exhibits how the rate changes if one switches from non-gaussian to gaussian character of the external noise.