Sentence examples for bifurcation value of system from inspiring English sources

Then (upsilon=0) is the Hopf bifurcation value of system (2).

Setting (tilde{u}(cdot,t)=u(cdot,tau t)), (tilde{v}(cdot,t)=v cdot,tau t)), (tilde{U}(t)= tilde{u}(cdot,t),tilde{v}(cdot,t))), and (tau=tau^{ast}+alpha) with (alphainmathbb{R}), then (alpha=0) is the Hopf bifurcation value of system (1).

Then (sigma=0 ) is a Hopf-bifurcation value of system (4).

Then (mu=0) is the Hopf bifurcation value of the system.

Then (mu=0) is the Hopf bifurcation value for system (2).

We use the center manifold theorem and bifurcation theory [19] to explore the fold bifurcation, flip bifurcation, and Naimark Sacker bifurcation of system (2).

In bifurcation diagrams, y-axis represents equilibria of state variable and x-axis represents value of system parameter that generates equilibria.

3, we discuss a codimension-one bifurcation (Neimark Sacker bifurcation and flip bifurcation) of system (2.3) at the fixed point.

Therefore, bifurcation diagrams reflect change in equilibria of dynamic systems (change in number of equilibria or change in numerical value of equilibria) in relation to change in numerical value of system parameters.

When b 1 exceeds the torus bifurcation value, the periodic orbit of the full system is stable (Figure 3a).

Guo et al. in [11] analyzed the fold and Hopf bifurcations, fold-Hopf bifurcations and Hopf-Hopf bifurcations of system (1.1) with (k=1), (g_{1}=g_{2}=f).