Results 211 to 220 of about 38,020 (248)

Anti-control of Hopf bifurcations

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2001
Summary: Bifurcation control generally means the design of a controller that is capable of modifying the bifurcation characteristics of a bifurcating nonlinear system, thereby achieving some desirable dynamical behaviors. A typical objective is to delay and/or stabilize an existing bifurcation. In this paper, we consider the problem of anti-controlling
Chen, Dong S., Wang, Hua O., Chen, Guanrong   +2 more
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Reversible Equivariant Hopf Bifurcation

Archive for Rational Mechanics and Analysis, 2004
This paper is devoted to the study of codimension-one reversible Hopf bifurcation; more precisely, the authors study periodic solutions near an equilibrium whose eigenvalues collide on the imaginary axis, where such a collision arises persistently in a one-parameter family. This situation is also known as 1:1 resonance.
Buzzi, Claudio Aguinaldo, Lamb, Jeroen S. W.   +1 more
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Stochastically perturbed hopf bifurcation

International Journal of Non-Linear Mechanics, 1987
A two-dimensional system of differential equations \[ \frac{dy}{dt}=F(y,\sigma)+\epsilon^{1/2}[A_ 1(\sigma)f(t)+A_ 2(\sigma)g(t)]y \] is considered where F is a vector function analytic in y and \(\sigma\), \(\sigma\) is a real-valued parameter, \(A_ 1(\sigma)\), \(A_ 2(\sigma)\) are \(2\times 2\)-matrices which depend only on \(\sigma\), f(t), g(t ...
Sri Namachchivaya, N., Ariaratnam, S. T.
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The Hopf Bifurcation

1979
Let X = Σ Xi∂i = Σ piξi∂i be a vectorfield on Δ. X is a function from Δ to RI. We define the Hessian of X at p, HPX: Tp Δ × Tp Δ → R to be the bilinear form defined by: $$ {H_P}X\left( {{Y^1}{Y^2}} \right) = {\left( {{d_P}X\left( {{Y^1}} \right),{Y^2}} \right)_P}. $$ (1.1) .
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Liouvillian dynamics of the Hopf bifurcation

Physical Review E, 2001
Two-dimensional vector fields undergoing a Hopf bifurcation are studied in a Liouville-equation approach. The Liouville equation rules the time evolution of statistical ensembles of trajectories issued from random initial conditions, but evolving under the deterministic dynamics.
Gaspard, Pierre, Tasaki, Shuichi
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Hopf bifurcation analysis in the system

Nonlinear Analysis: Real World Applications, 2010
The authors study Hopf bifurcation for the T system, which is a Lorenz-like system. By using results from the normal form theory, the direction of this bifurcation and the stability of the emerging periodic orbits are given. The paper ends with some numerical illustrations.
Jiang, Bo, Han, Xiujing, Bi, Qinsheng
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On the Andronov–Hopf Bifurcation Theorem

Differential Equations, 2001
Based on the introduced notion of a 2-regular nonlinear mapping at a singular point, the author suggests a new proof of the known Andronov-Hopf bifurcation theorem.
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HOPF Bifurcation for Periodic Systems

1985
This paper concerns with the problem of Hopf bifurcation from an equilibrium position to periodic solutions, in the case of n dimensional periodic differential systems. Results about existence and uniqueness of bifurcating periodic solutions are obtained.
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Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems

Physics Reports, 2022
David J W Simpson
exaly  

Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation

Mathematics and Computers in Simulation, 2021
Changjin Xu, Maoxin Liao, Peiluan Li
exaly