On the Consequence of Blow-Out Bifurcations

초록

We investigate the consequence of a blow-out bifurcation of a chaotic attractor in an invariant line in a family of piecewise linear planar maps by changing a positive parameter β controlling the reinjection. Through a supercritical blow-out bifurcation, a chaotic or hyperchaotic attractor, exhibiting on-off intermittency, is born, depending on the value of β. For large β, a hyperchaotic attractor with a positive second Lyapunov exponent appears. However, as the parameter β decreases and passes a threshold value β*, a transition from hyperchaos to chaos occurs. Hence, for 0 < β < β* a chaotic attractor with a negative second Lyapunov exponent is born. The sign of the second Lyapunov exponent of the newly-born intermittent attractor is found to be determined through competition between its laminar and bursting components. When the "strength" (i.e., a weighted second Lyapunov exponent) of the bursting component is larger (smaller) than that of the laminar component, a hyperchaotic (chaotic) attractor appears.

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