A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits
نویسندگان
چکیده
منابع مشابه
A stochastic pitchfork bifurcation in a reaction-diffusion equation
First we prove, for m 65, a lower bound on the dimension of the random attractor, which is of the same order in as the upper bound we derived in an earlier paper, and is the same as that obtained in the deterministic case. Then we show, for m = 1, that as passes through ¶ 1 (the rst eigenvalue of the negative Laplacian) from below, the system undergoes a stochastic bifurcation of pitchfor...
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The bifurcations of strange nonchaotic attractors in quasi-periodically forced systems are poorly understood. A simple two-parameter example is introduced which unifies previous observations of the non-smooth pitchfork bifurcation. There are two types of generalized pitchfork bifurcation which occur in this example, and the corresponding bifurcation curves can be calculated analytically. The ex...
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We present an algorithm for computing the direction of pitchfork bifurcation for two-point boundary value problems. The formula is rather involved, but its computational evaluation is quite feasible. As an application, we obtain a multiplicity result.
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In nonintegrable Hamiltonian systems with mixed phase space and discrete symmetries, sequences of pitchfork bifurcations of periodic orbits pave the way from integrability to chaos. In extending the semiclassical trace formula for the spectral density, we develop a uniform approximation for the combined contribution of pitchfork bifurcation pairs. For a two-dimensional double-well potential and...
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ژورنال
عنوان ژورنال: International Journal of Bifurcation and Chaos
سال: 2018
ISSN: 0218-1274,1793-6551
DOI: 10.1142/s0218127418500177