Bifurcation

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Bifurcation

When a non-linear dynamic system develops twice the possible solutions that it had before it passed its critical level. A bifurcation cascade is often called the period doubling route to chaos because the transition from an orderly system to a chaotic system often occurs when the number of possible solutions begins increasing, doubling each time.
References in periodicals archive ?
Hopf bifurcations in a reaction-diffusion population model with delay effect.
The significance of developing models for arterial bifurcations relate to the fact that disease mostly occurs near arterial bifurcations.
In this study, the effects of [[bar.g].sub.Na] and [[bar.g].sub.K] on the stability and bifurcations of the model will be discussed, respectively, and collectively.
System (20a), (20b), (20c), and (20d) undergoes 3 different codimension-1 bifurcations: saddle-node bifurcation, equilibrium transition, and nonsmooth fold bifurcation.
Holmes, "Bifurcations to divergence and flutter in flow-induced oscillations: a finite dimensional analysis," Journal of Sound and Vibration, vol.
In our work, we provide a new idea to investigate the behavior, similar to continuous situation, by calculating normal form coefficients and finding the n-order focal values or Lyapunov coefficients [7, 19, 22, 27]; this is the first attempt to link limit cycles theory of continuous models with discrete models' invariant closed curves bifurcations by normal form coefficients and Lyapunov coefficients.
Wang, "Imperfect transcritical and pitchfork bifurcations," Journal of Functional Analysis, vol.
In the 2D bifurcation diagrams, the system exhibits a sequence of flip bifurcations to chaos (which means that the market will fall into chaos), then to divergence at last (which means the players will be out of the market).
From the bifurcation diagram depicted in Figure 2, we can see that the period of the ensemble mean response (EMR) varies from 1T to 2T and then to 4T and finally period-doubling bifurcations lead to chaos as the fractional-order q varies.
This is likely due to the proximal spread of local anesthetic that was observed in this investigation and may be occurring in patients with more distal SN bifurcations. Further studies should be aimed at stratifying patients based on bifurcation length and the analgesic benefit of lower volumes of injectate.