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On the Definitions of Bifurcation
International Journal of Bifurcation and Chaos, 1997In this paper the equivalence of two definitions of elementary bifurcation is proved and a new definition for bifurcation is given.
K. Zhou, J. K. Wu
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Modeling, Analysis and Bifurcation Control of a Delayed Fractional-Order Predator-Prey Model
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2018This paper basically concentrates on the bifurcation control of a fractional delayed predator–prey system via feedback control methodology. Firstly, time delay is regarded as a bifurcation parameter, and the delay-induced bifurcation conditions for such ...
Chengdai Huang +4 more
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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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OBSERVABILITY BIFURCATION VERSUS OBSERVING BIFURCATIONS
IFAC Proceedings Volumes, 2002Abstract In this paper we highlight the difference between observability bifurcation and observing bifurcation. From this, we deduce that one way to improve transmission by synchronization of chaotic systems may be chaotic transmitter with also observability bifurcation.
Driss Boutat +3 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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Bifurcation Properties for Fractional Order Delayed BAM Neural Networks
Cognitive Computation, 2021Changjin Xu +4 more
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The bifurcation and secondary bifurcation of capillary-gravity waves
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1985The bifurcation and secondary bifurcation of capillary-gravity waves is analysed when the surface tension is close to or equal to a value where the eigenspace of the critical phase speed has multiplicity two. The existence and multiplicity of solutions is seen, via the implicit function theorem, to be a special case of the secondary bifurcation ...
John Toland, M. C. W. Jones
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Nonlinear Analysis: Theory, Methods & Applications, 1992
Throughout this paper we consider the following nonlinear eigenvalue problem: \[ \Delta u(x) + q(x) | u(x) |^ \sigma u(x) + \lambda u(x) = 0 \quad \text{for} \quad x \in \mathbb{R}^ N,\;u \in H^ 1(\mathbb{R}^ N) \setminus \{0\}. \tag{1} \] For each \(\lambda \in \mathbb{R}\), \(u \equiv 0\) is a solution of equation (1) and the spectrum of the ...
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Throughout this paper we consider the following nonlinear eigenvalue problem: \[ \Delta u(x) + q(x) | u(x) |^ \sigma u(x) + \lambda u(x) = 0 \quad \text{for} \quad x \in \mathbb{R}^ N,\;u \in H^ 1(\mathbb{R}^ N) \setminus \{0\}. \tag{1} \] For each \(\lambda \in \mathbb{R}\), \(u \equiv 0\) is a solution of equation (1) and the spectrum of the ...
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Bifurcation of Elastic Multilayers
2013The occurrence of a bifurcation in a multilayer structure during loading sets a limit on its deformability, and therefore represents an important factor in the design of composites. Since bifurcationis strongly influenced by the contact conditions at the interfaces between the layers, the mechanical modeling of these conditions is crucial.
Bigoni, Davide +2 more
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