Pitchfork and Hopf bifurcation threshold in stochastic equations with delayed feedback

Pitchfork and Hopf bifurcation thresholds in stochastic equations with delayed feedback

The bifurcation diagram of a model stochastic differential equation with delayed feedback is presented. We are motivated by recent research on stochastic effects in models of transcriptional gene regulation. We start from the normal form for a pitchfork bifurcation, and add multiplicative or parametric noise and linear delayed feedback. The latter is sufficient to originate a Hopf bifurcation in that region of parameters in which there is a sufficiently strong negative feedback. We find a sharp bifurcation in parameter space, and define the threshold as the point in which the stationary distri…

Controlling the transition between the Turing and antispiral patterns by using time-delayed-feedback

The controllable transition between the Turing and antispiral patterns is studied by using time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as perturbation and analyze the effect of the time delay on the Turing and Hopf instabilities near the Turing-Hopf codimension-two phase space. Numerical simulations show the transition between the Turing patterns (hexagon, stripe, and honeycomb), the dual-mode antispiral, and the antispiral by applying appropriate feedback parameters. The dual-mode antispiral pattern originates from the competition between the Turing and …

噪声存在下极限环的合并

Coalescence of limit cycles in the presence of noise

本文研究噪声对极限环在例外点合并分岔附近动力学的影响，通过Hopf振子范式建模并与叉形分岔耦合，建立标度理论，发现相位-相位关联具普适标度的非扩散行为。

Pattern formation in a two-component reaction-diffusion system with delayed processes on a network

Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us get explicit analytic conditions for the onset of patterns as a function of the main involved parameters, the time-delay, the network topology and the diffusion coefficients. Depending on these parameters, the analysis predicts whether the system will evolve towards a stationary Turing pattern or rather to a wave pattern associated to a Hopf bifurcation. The possible outcomes of the linear analysis overc…

Time-delayed feedback control of the Dicke-Hepp-Lieb superradiant quantum phase transition

We apply the time-delayed Pyragas control scheme to the dissipative Dicke model via a modulation of the atom-field-coupling. The feedback creates an infinite sequence of non-equilibrium phases with fixed points and limit cycles in the primary superradiant regime. We analyse this Hopf bifurcation scenario as a function of delay time and feedback strength, and determine analytical conditions for the phase boundaries.

活性流体中集体状态之间稀有转变的分析

Rare transitions between collective states in an active fluid via a weakly nonlinear reduction

本文研究了稀释悬浮液中杆状粒子在斯托克斯流中游泳的动力学，通过弱非线性展开分析粒子扩散率降低时的双稳态转变，利用随机噪声驱动揭示集体运动中稀有状态转换机制。