Nonequilibrium Phenomena in Globally Coupled Phase Oscillators: Noise-Induced Bifurcations, Clustering, and Switching

1997 ◽  
Vol 07 (04) ◽  
pp. 917-922
Author(s):  
Seon Hee Park ◽  
Seunghwan Kim ◽  
Seung Kee Han
Keyword(s):  
Phase Transition ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Critical Value ◽  
Phase Oscillators ◽  
Deterministic Systems ◽  
Nonequilibrium Phenomena ◽  
Noise Models ◽  
Coupled Phase Oscillators

The Nonequilibrium phenomena in a class of globally coupled phase oscillators systems with multiplicative noise are studied. It is shown that at the critical value of the noise intensity the systems undergo a phase transition and converge to clustered states. We also show that the time delay in the interaction between oscillators gives rise to the switching phenomena of clusters. These phenomena are noise-induced effects which cannot be seen in the deterministic systems or in the simple additive noise models.

UPPER BOUND OF THE TIME DERIVATIVE OF ENTROPY FOR A DYNAMICAL SYSTEM DRIVEN BY TWO KINDS OF COLORED NOISE

2009 ◽  
Vol 23 (02) ◽  
pp. 199-207 ◽  
Author(s):  
CAN-JUN WANG ◽  
DONG-CHENG MEI
Keyword(s):  
Dynamical System ◽  
Upper Bound ◽  
Correlation Time ◽  
Noise Intensity ◽  
Cross Correlation ◽  
Colored Noise ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Time Derivative ◽  
The Cross

The upper bound UB(t) of the time derivative of entropy for a dynamical system driven by both additive colored noise and multiplicative colored noise with colored cross-correlation is investigated. Based on the Fokker–Planck equation, the effects of the parameters on UB(t) are analyzed. The results show that: (i) α (the multiplicative noise intensity), D (the additive noise intensity) and τ2 (the correlation time of the additive noise) always enhance UB (t) monotonically; (ii) λ (the intensity of the cross-correlation between the multiplicative noise and the additive noise), τ1 (the correlation time of the multiplicative noise), τ3 (the correlation time of the cross-correlation) and γ (the dissipative constant) all possess a minimum, i.e., UB (t) decreases for small values and increases for large values.

Stochastic dynamic behavior of FitzHugh–Nagumo neurons stimulated by white noise

2021 ◽  
pp. 2150137
Author(s):  
Tao Li ◽  
Kaijun Wu ◽  
Mingjun Yan ◽  
Zhengnan Liu ◽  
Huan Zheng
Keyword(s):  
Stochastic Resonance ◽  
Bifurcation Point ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Coherence Resonance ◽  
Resonance Behavior ◽  
Additive And Multiplicative Noise ◽  
Coherent Resonance ◽  
Resonance Coefficient

Stochastic noise exists widely in the nervous system, and noise plays an extremely important role in the information processing of the nervous system. Noise can enhance the ability of neurons to process information as well as decrease it. For the dynamic behavior of stochastic resonance and coherent resonance shown by neurons under the action of stochastic noise, this paper uses Fourier coefficient and coherence resonance coefficient to measure the behavior of stochastic resonance and coherence resonance, respectively, and some conclusions are drawn by analyzing the effects of additive noise and multiplicative noise. Appropriate noise can make the nonlinear system exhibit stochastic resonance behavior and enhance the detection ability of external signals. It can also make the coherent resonance behavior of the nonlinear system reach its optimal state, and the system becomes more orderly. By comparing the effects of additive and multiplicative noise on the stochastic resonance behavior and coherent resonance behavior of the system, it is found that additive and multiplicative noise can both make the system appear the phenomenon of stochastic resonance and have almost identical discharge state at the same noise intensity. However, with the increase of noise intensity, the coherent resonance of the system occurs, the multiplicative noise intensity is smaller than that of additive noise, but the coherent resonance coefficient of additive noise is smaller and the coherent resonance effect is better. The system whose system parameters are located near the bifurcation point is more prone to coherent resonance, and the closer the bifurcation point is, the more obvious the coherent resonance phenomenon is, and the more regular the system becomes. When the parameters of the system are far away from the bifurcation point, the coherent resonance will hardly appear. Besides, when additive and multiplicative noise interact together, the stochastic resonance and coherent resonance phenomena are more likely to appear at small noise, and the behavior of stochastic resonance and coherent resonance that the system shown is better in the local range.

The analysis of particles behavior under a delayed tristable system driven by multiplicative and additive noises

2021 ◽  
pp. 2150219
Author(s):  
Gang Zhang ◽  
Yichen Shu ◽  
Tianqi Zhang
Keyword(s):  
Time Delay ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Brownian Particle ◽  
Gaussian White Noise ◽  
Equilibrium Phase ◽  
Stable State ◽  
Planck Equation ◽  
Correlation Strength

In this paper, the motion of Brownian particles driven by a delayed tristable system with multiplicative and additive Gaussian white noise is mainly studied. First, the effective potential function and stable state probability density function (PDF) are derived by using the theory of small-time delay approximation and the approximate Fokker–Planck equation (FPE), and the expression of mean first-passage times (MFPTs) is obtained by using the definition of the MFPTs and the steepest descent method. Then, the effects of the parameters which include noise intensities of multiplicative and additive noise, and correlation strength between two noises, and time delay, and the strength of time-delayed feedback on PDF and MFPTs are analyzed. Results demonstrate that the additive noise intensity has a more profound influence on PDF than the multiplicative noise intensity. The non-equilibrium phase transition of the system can be produced by the correlation strength of noises. In addition, in the behavior of the MFPTs, we can observe the noise-enhanced stability (NES) phenomenon induced by multiplicative noise intensity. Besides, delayed time plays an important role in MFPTs. Moreover, MFPT [Formula: see text] (stands for the Brownian particle moving from the left well to the middle well) is greater than [Formula: see text] (stands for the Brownian particle moving from the middle well to the left one).

The flattening phase transition in systems of trapped ions

2009 ◽  
Vol 87 (10) ◽  
pp. 1425-1435 ◽  
Author(s):  
Taunia L. L. Closson ◽  
Marc R. Roussel
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Order Parameter ◽  
Ion Trap ◽  
Anisotropy Parameter ◽  
Critical Value ◽  
Trapped Ions ◽  
Dimensional Structure ◽  
Flattening Process ◽  
Second Order Phase Transition

When the anisotropy of a harmonic ion trap is increased, the ions eventually collapse into a two-dimensional structure consisting of concentric shells of ions. This collapse generally behaves like a second-order phase transition. A graph of the critical value of the anisotropy parameter vs. the number of ions displays substructure closely related to the inner-shell configurations of the clusters. The critical exponent for the order parameter of this phase transition (maximum extent in the z direction) was found computationally to have the value β = 1/2. A second critical exponent related to displacements perpendicular to the z axis was found to have the value δ = 1. Using these estimates of the critical exponents, we derive an equation that relates the amplitudes of the displacements of the ions parallel to the x–y plane to the amplitudes along the z axis during the flattening process.

Laser-Induced Pretransitional Ordering And Nonlinear Optical Properties Of Rigid-Rod Polymer Suspensions

1993 ◽  
Vol 328 ◽  
Author(s):  
Boris E. Vugmeister ◽  
Michelle S. Malcuit ◽  
John C. Kralik ◽  
Colleen Stevens
Keyword(s):  
Phase Transition ◽  
Colloidal Particles ◽  
Volume Fraction ◽  
Orientational Order ◽  
Critical Value ◽  
Orientational Relaxation ◽  
First Order ◽  
First Order Phase Transition ◽  
Rigid Rod ◽  
First Order Phase

ABSTRACTWe investigate the pretransitional behavior in laser-induced alignment of rigid rod-like polytetraflouroethylene (PTFE) suspensions. Using a laser-induced birefringence experiment, we measure both the orientational order parameter and the orientational relaxation time. We find that both increase as the volume fraction of colloidal particles approaches the critical value for the isotropic-nematic phase transition. Experimental results are compared with theory which takes into account the possibility of a first-order phase transition induced by a laser electric field.

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