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Periodically Perturbed Bifurcation. II. Hopf Bifurcation
Studies in Applied Mathematics, 1981We consider the effect of a periodic perturbation on the bifurcation behavior of a system of differential equations. It is shown that periodic solutions are, in general, modified into quasiperiodic solutions. Different phenomena are encountered in resonance and near‐resonance conditions, leading in some cases to separation of solution branches and in ...
Rosenblat, S., Cohen, Donald S.
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Periodically Perturbed Bifurcation—1. Simple Bifurcation
Studies in Applied Mathematics, 1980We consider the effect of a periodic perturbation on the bifurcation behavior of a system of differential equations. It is shown that constant solutions are modified into periodic solutions, and that the perturbations leads to the separation of solution branches.
Rosenblat, S., Cohen, Donald S.
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A novel strategy of bifurcation control for a delayed fractional predator-prey model
Applied Mathematics and Computation, 2019This paper aims at controlling bifurcation of a fractional predator–prey system by an original extended delayed feedback controller. Firstly, some sufficient conditions of delay-induced bifurcations for such uncontrolled system are captured regarding ...
Chengdai Huang, Huan Li, Jinde Cao
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Control of the Hopf bifurcation in the Takens-Bogdanov bifurcation
2008 47th IEEE Conference on Decision and Control, 2008It is a well-known result that in a versal deformation of the Takens-Bogdanov bifurcation is possible to find dynamical systems that undergo saddle-node, homoclinic and Hopf bifurcations. In this document a nonlinear control system in the plane is considered, whose nominal vector field undergoes the Takens-Bogdanov bifurcation, and then the idea is to ...
Francisco Armando Carrillo Navarro +1 more
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Journal of the Franklin Institute, 2019
In this paper, a delayed fractional eco-epidemiological model with incommensurate orders is proposed, and a control strategy of this model is discussed.
Xinhe Wang, Zhen Wang, Jianwei Xia
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In this paper, a delayed fractional eco-epidemiological model with incommensurate orders is proposed, and a control strategy of this model is discussed.
Xinhe Wang, Zhen Wang, Jianwei Xia
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To Bifurcate or Not To Bifurcate? That is the (Ambiguous) Question
Arbitration International, 2013Commentators and practitioners hold different views about ‘bifurcation’, i.e. the procedural technique of splitting the arbitral proceedings in distinct phases with a view of reaching decisions on discrete matters. The discussion mostly focuses on whether bifurcation is a source of efficiency or rather of useless additional costs and delays.
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1999
Abstract The solutions are real for λ 3 and λ 1, and complex for 3 < λ < 1. The graphs of Re(m1) and Re(m2) against λ are shown in Figure 12.1. Noting the signs of m1 and m2, we can observe that the equilibrium point at the origin is: A bifurcation occurs at the parametric value λ 1 where, as λ increases, the equilibrium ...
D W Jordan, P Smith
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Abstract The solutions are real for λ 3 and λ 1, and complex for 3 < λ < 1. The graphs of Re(m1) and Re(m2) against λ are shown in Figure 12.1. Noting the signs of m1 and m2, we can observe that the equilibrium point at the origin is: A bifurcation occurs at the parametric value λ 1 where, as λ increases, the equilibrium ...
D W Jordan, P Smith
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International Journal of Bifurcation and Chaos, 2007
The coalescence of a Hopf bifurcation with a codimension-two cusp bifurcation of equilibrium points yields a codimension-three bifurcation with rich dynamic behavior. This paper presents a comprehensive study of this cusp-Hopf bifurcation on the three-dimensional center manifold.
John Harlim, William F. Langford
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The coalescence of a Hopf bifurcation with a codimension-two cusp bifurcation of equilibrium points yields a codimension-three bifurcation with rich dynamic behavior. This paper presents a comprehensive study of this cusp-Hopf bifurcation on the three-dimensional center manifold.
John Harlim, William F. Langford
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Border-collision bifurcations: An explanation for observed bifurcation phenomena
Physical Review E, 1994Recently physical and computer experiments involving systems describable by continuous maps that are nondifferentiable on some surface in phase space have revealed novel bifurcation phenomena. These phenomena are part of a rich new class of bifurcations which we call border-collision bifurcations.
Nusse, Helena E. +2 more
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Bifurcation Mechanism for Fractional-Order Three-Triangle Multi-delayed Neural Networks
Neural Processing Letters, 2022Changjin Xu +4 more
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