Results 271 to 280 of about 5,272,693 (342)

Computing multiple pitchfork bifurcation points

Computing, 1997
For the parameter dependent nonlinear equation \(F(x,\lambda) =0\), \(F: \mathbb{R}^n \times \mathbb{R}^1 \to\mathbb{R}^n\), the generically important case \(\text{rank} \partial_x E(x^*, \lambda^*) =n-1\) is investigated. In a neighborhood of such pitchfork bifurcation point \((x^*, \lambda^*)\) of multiplicity \(p\geq 1\) the Lyapunov-Schmidt ...
Pönisch, G., Schnabel, U., Schwetlick, H.   +2 more
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The Computation of Symmetry-Breaking Bifurcation Points

SIAM Journal on Numerical Analysis, 1984
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Werner, B., Spence, A.
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A numerical approach to hopf bifurcation points

Journal of Shanghai University (English Edition), 1998
Consider the \(n\)-dimensional autonomous system \({dx\over dt}= f(x,\alpha)\) depending on a real parameter \(\alpha\). The authors present a numerical method to detect a Hopf bifurcation point \(\alpha_0\) based on the computation of the largest Lyapunov exponent. The method is illustrated by means of two examples.
Yang, Zhonghua, Li, Changpin
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Bifurcation and Critical Point

2012
In Chap. 4, we use bifurcation and critical point theory together to study the structure of the solutions of elliptic equations; also we have results on three sign-changing solutions.
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Degenerate Transcritical Bifurcation Point can be an Attractor: A Case Study in a Slow–Fast Modified Leslie–Gower Model

Qualitative Theory of Dynamical Systems, 2022
Liyan Zhong, Jianhe Shen
semanticscholar   +1 more source

Bifurcation and Controller Design of 5D BAM Neural Networks With Time Delay

International journal of numerical modelling
All the time delayed dynamical system plays a vital role in describing the dynamical phenomenon of neural networks. In the current article, we study a class of 5D delayed bidirectional associative memory (BAM) neural networks that conform to objective ...
Qing Cui, Changjin Xu, Yiya Xu, Wei-Bo Ou, Yicheng Pang, Zixin Liu, Jianwei Shen, M. Baber, C. Maharajan, Uttam Ghosh   +9 more
semanticscholar   +1 more source

Investigation of bifurcation points

1969
In sections 16 and 17 we encountered bifurcation points. In diagrams which represent the solutions depending on some parameter e, say, there exist special values of this parameter, es, where solutions coincide which for e ≠ es are of different character. Looked at e = es from another point of view we might say that at e = es a new solution branches off
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Undecidable hopf bifurcation with undecidable fixed point

International Journal of Theoretical Physics, 1994
Motivated by Hilbert's sixth problem and its contemporary revisions by V. I. Arnold [\textit{F. E. Browder}: ``Problems of present day mathematics'', Math. developments arising from Hilbert problems, Proc. Symp. Pure Math. 28, 35-79 (1976; Zbl 0326.00002), p.
da Costa, N. C. A., Doria, F. A.
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Anticipatory Systems near Bifurcation Points

AIP Conference Proceedings, 2006
Bifurcation in the sense of applied mathematics happens when the system is on the boundary of one set of equivalent states. Generally a system undergoing bifurcation is in a critical state. Any small change in the parameters may result essentially different behaviors.
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The homoclinic twist bifurcation point

1992
We analyze bifurcations occurring in the vicinity of a homoclinic twist point for a generic two parameter family of Z 2 equivariant ODE’s in four dimensions. The results are compared with numerical results for a system of two coupled Josephson junctions with pure capacitive load.
Aronson, D.G., van Gils, S.A., Krupa, M.
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