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Amplification of magnetic field effects <i>via</i> critical dynamics in a nonlinear oscillatory system. [PDF]
Chem SciZhang S +4 more
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Period-doubling cascade to chaos and optimal quadratic harvesting in a prey-predator-scavenger model using Crowley-Martin functional response. [PDF]
Sci RepManoharan R +4 more
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Physica D: Nonlinear Phenomena, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hirschberg, P., Knobloch, E.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hirschberg, P., Knobloch, E.
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SIAM Journal on Numerical Analysis, 1997
Summary: This paper addresses the problems of detecting Hopf bifurcations in systems of ordinary differential equations and following curves of Hopf points in two-parameter families of vector fields. The established approach to this problem relies upon augmenting the equilibrium condition so that a Hopf bifurcation occurs at an isolated, regular point ...
Guckenheimer, John +2 more
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Summary: This paper addresses the problems of detecting Hopf bifurcations in systems of ordinary differential equations and following curves of Hopf points in two-parameter families of vector fields. The established approach to this problem relies upon augmenting the equilibrium condition so that a Hopf bifurcation occurs at an isolated, regular point ...
Guckenheimer, John +2 more
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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.
Harlim, J., Langford, W. F.
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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.
Harlim, J., Langford, W. F.
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Periodically Perturbed Hopf Bifurcation
SIAM Journal on Applied Mathematics, 1987A general two-dimensional system of differential equations with periodic parametric excitation is considered with two real parameters one of them being the amplitude of the periodic excitation. As a matter of fact, the frequency of the excitation occurs also as an additional parameter, and in this respect the paper is related to the reviewer's results [
Sri Namachchivaya, N., Ariaratnam, S. T.
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On Generalized Hopf Bifurcations
Journal of Dynamic Systems, Measurement, and Control, 1984Two distinct degenerate Hopf bifurcation phenomena associated with autonomous lumped-parameter systems are explored in great detail via the intrinsic harmonic balancing method. It is assumed that the Hopf’s transversality condition is violated and certain other conditions prevail.
Huseyin, K., Atadan, A. S.
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Reversible Equivariant Hopf Bifurcation
Archive for Rational Mechanics and Analysis, 2004This 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 +1 more
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Stochastically perturbed hopf bifurcation
International Journal of Non-Linear Mechanics, 1987A 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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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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