Results 11 to 20 of about 228,096 (272)
Hopf bifurcation with additive noise [PDF]
Nonlinearity, 2017 We consider the dynamics of a two-dimensional ordinary differential equation exhibiting a Hopf bifurcation subject to additive white noise and identify three dynamical phases: (I) a random attractor with uniform synchronisation of trajectories, (II) a ...
T. S. Doan +3 more
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A stochastic Hopf bifurcation [PDF]
Probability Theory and Related Fields, 1994 Let \(\{x_ t : t \geq 0 \}\) be the solution of a stochastic differential equation (SDE) in \(\mathbb{R}^ d\) which fixes 0, and let \(\lambda\) denote the Lyapunov exponent for the linear SDE obtained by linearizing the original SDE at 0. It is known that, under appropriate conditions, the sign of \(\lambda\) controls the stability/instability of 0 ...
Peter H. Baxendale
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Control of dynamic Hopf bifurcations [PDF]
Nonlinearity, 1999 The slow passage through a Hopf bifurcation leads to the delayed appearance of large amplitude oscillations. We construct a smooth scalar feedback control which suppresses the delay and causes the system to follow a stable equilibrium branch. This feature can be used to detect in time the loss of stability of an ageing device.
Nils Berglund
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Are physiological oscillations physiological?
The Journal of Physiology, EarlyView., 2023 Abstract figure legend Mechanisms and functions of physiological oscillations. Abstract Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function.
Lingyun (Ivy) Xiong, Alan Garfinkel
wiley +1 more source
Mathematical Biosciences and Engineering, 2023 In this paper, a fractional-order two delays neural network with ring-hub structure is investigated. Firstly, the stability and the existence of Hopf bifurcation of proposed system are obtained by taking the sum of two delays as the bifurcation parameter.
Yuan Ma, Yunxian Dai
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Hopf bifurcations on cubic lattices [PDF]
Nonlinearity, 2003 The author continues his previous work in this article. The standard results on equivariant Hopf bifurcation are applied. Explicit computations concerning stability are performed.
T. K. Callahan
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Optimization of Hopf Bifurcation Points
SIAM Journal on Scientific Computing, 2023 We introduce a numerical technique for controlling the location and stability properties of Hopf bifurcations in dynamical systems. The algorithm consists of solving an optimization problem constrained by an extended system of nonlinear partial differential equations that characterizes Hopf bifurcation points.
Nicolas Boullé +2 more
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Turing Instability and Turing–Hopf Bifurcation in Diffusive Schnakenberg Systems with Gene Expression Time Delay [PDF]
Journal of Dynamics and Differential Equations, 2018 In this paper, we study the delayed reaction–diffusion Schnakenberg systems with Neumann boundary conditions. Sufficient and necessary conditions for the occurrence of Turing instability are obtained, and the existence of Turing, Hopf and Turing–Hopf ...
Weihua Jiang, Hongbin Wang, Xun Cao
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Energy Science & Engineering, 2023 The strong coupling, multivariate, and nonlinear characteristics of the mathematical model of a doubly‐fed induction generator (DFIG) make it challenging to analyze the bifurcation category of the DFIG. Therefore, in this study, we developed a method for
Wei Chen +4 more
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Bifurcation phenomena in a single-species reaction-diffusion model with spatiotemporal delay
AIMS Mathematics, 2021 In this paper we investigate bifurcation phenomena in a single-species reaction-diffusion model with spatiotemporal delay under the conditions of the weak and strong kernel functions.
Gaoxiang Yang, Xiaoyu Li
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