Cascades of period doubling bifurcations: a prerequisite for horseshoes.From theCambridge English Corpus
Connected simple systems, transition matrices and heteroclinic bifurcations.From theCambridge English Corpus
On some global bifurcations connected with disappearance of a saddle-node fixed point.From theCambridge English Corpus
General bifurcations from periodic solutions with spatiotemporal symmetry, including mode interactions and resonances, in preparation.From theCambridge English Corpus
Further increase of the wave amplitude leads to further bifurcations and eventually to a chaotic surface agitation.From theCambridge English Corpus
However, qualitative analysis of equilibria, bifurcations or asymptotic behaviour is more difficult than with differential equation models.From theCambridge English Corpus
We discuss the dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of random diffeomorphisms.From theCambridge English Corpus
The following local bifurcations can be found by straightforward calculations.From theCambridge English Corpus
He gave properties of the non-wandering set, traced the genealogies of the periodic points of period 5, and described their stability types and bifurcations.From theCambridge English Corpus
Much of the original motivation for developing the theory of bifurcations with symmetry came from fluid mechanical experiments in the laboratory.From theCambridge English Corpus
The rather short length of the vortex is characteristic of the disturbance for symmetrybreaking pitchfork bifurcations.From theCambridge English Corpus
Morphological bifurcations involving reaction-diffusion processes during microtubule formation.From theCambridge English Corpus
Also, complicated price dynamics can only be generated through saddle-nodetype bifurcations.From theCambridge English Corpus
We can reduce the problem of detecting bifurcations one step further, by noting the following.From theCambridge English Corpus
Typically, transition to chaos takes place through bifurcations.From theCambridge English Corpus
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