In the previous section, we have shown that system (3.1) undergoes a flip (period-doubling) bifurcation when ( p, q ) ∈ L 1 and a Neimark-Sacker bifurcation when ( p, q ) ∈ L 3 at equilibrium point X ∗.
In the previous section, we have shown that system (3.1) undergoes a flip (period-doubling) bifurcation when ((p,q in L_{1}) and a Neimark-Sacker bifurcation when ((p,q in L_{3}) at the equilibrium point (X^).
By applying center manifold theory, we find and prove the existence of a transcritical bifurcation at a disease-free equilibrium point and flip bifurcation (or period-doubling bifurcation) at a positive endemic equilibrium point.
(Note that in this paper, the words flip bifurcation and period doubling bifurcation are used interchangeably).
Tennessee showed resolve winning in overtime at Giants Stadium on Sunday even though it lost the coin flip for the overtime period and was forced to stop the Giants' offense before driving for the winning field goal.
In Section 3, we study the existence of Neimark-Sacker and period doubling (flip) bifurcation for this system by analyzing the characteristic equation.
We prove that there exist two bifurcations for this system by analyzing the characteristic equation: (1) Neimark-Sacker bifurcation, (2) period doubling (flip) bifurcation.
In Section 3 we prove the existence of Neimark-Sacker and period doubling (flip) bifurcation for this system by analysing the characteristic equation, and then in Section 4 we investigate the direction of this bifurcations by using normal form theory. Finally in Section 5 we give numerical simulations to support our theoretical analysis.
Further more we prove the existence of Neimark-Sacker and period doubling (flip) bifurcation for this system by analysing the characteristic equation, and investigate the direction of this bifurcations by using normal form theory. Finally some numerical simulations are carried out to support the analytical results.
With the score tied at 3-3 late in the second period, he lay out to stop two straight point-blank shots late in the second period, flipping his body as if he were defending both sides of the bed.
Being submerged for an extended period flips a primordial, water-mammalian switch, she says.
