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