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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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A stochastic Hopf bifurcation [PDF]
Probability Theory and Related Fields, 1994 Let {x t :t≧0} be the solution of a stochastic differential equation (SDE) in ℝ d which fixes 0, and let λ denote the Lyapunov exponent for the linear SDE obtained by linearizing the original SDE at 0.
Peter H. Baxendale
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THE HOPF BIFURCATION WITH BOUNDED NOISE. [PDF]
Discrete Contin Dyn Syst Ser A, 2012 We study Hopf-Andronov bifurcations in a class of random differential equations (RDEs) with bounded noise. We observe that when an ordinary differential equation that undergoes a Hopf bifurcation is subjected to bounded noise then the bifurcation that occurs involves a discontinuous change in the Minimal Forward Invariant set.
Botts RT, Homburg AJ, Young TR.
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Hopf bifurcations on cubic lattices [PDF]
Nonlinearity, 2003 We analyze three-dimensional pattern forming Hopf bifurcations with the spatial periodicity of the face-centered (FCC) and body-centered (BCC) cubic lattices. This is an equivariant bifurcation with spatial symmetry Γ = T 3∔O⊕ℤ3. By extending the group to a larger, wreath product group we can use the method of 5 to find all solution branches guaranteed
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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Influence of Coil Current and Oil Film Thickness on Hopf Bifurcation of MLDSB
Energies, 2022 Magnetic-liquid double-suspension bearing (MLDSB) is composed of an electromagnetic supporting system and a hydrostatic supporting system. Due to its greater supporting capacity and stiffness, it is appropriate for middle-speed applications, overloading,
Jianhua Zhao +6 more
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Bogdanov–Takens bifurcation of a Holling IV prey–predator model with constant-effort harvesting
Journal of Inequalities and Applications, 2021 A prey–predator model with constant-effort harvesting on the prey and predators is investigated in this paper. First, we discuss the number and type of the equilibria by analyzing the equations of equilibria and the distribution of eigenvalues.
Lifang Cheng, Litao Zhang
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Cluster Oscillation of a Fractional-Order Duffing System with Slow Variable Parameter Excitation
Fractal and Fractional, 2022 The complicated dynamic behavior of a fractional-order Duffing system with slow variable parameter excitation is investigated. The stability and bifurcation behavior of the fast subsystem are analyzed by using the dynamic theory of fractional-order ...
Xianghong Li, Yanli Wang, Yongjun Shen
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Advances in Difference Equations, 2020 In this paper, stochastic Hopf–Hopf bifurcation of the discrete coupling logistic system with symbiotic interaction is investigated. Firstly, orthogonal polynomial approximation of discrete random function in the Hilbert spaces is applied to reduce the ...
Maosong Yang, Shaojuan Ma
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Hopf bifurcation in delayed nutrient-microorganism model with network structure
Journal of Biological Dynamics, 2022 In this paper, we introduce and deal with the delayed nutrient-microorganism model with a random network structure. By employing time delay τ as the main critical value of the Hopf bifurcation, we investigate the direction of the Hopf bifurcation of such
Mengxin Chen +3 more
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