ZhETF, Vol. 145,
p. 565 (March 2014)
(English translation - JETP,
Vol. 118, No. 3,
available online at www.springer.com
BISTABILITY IN A HYPERCHAOTIC SYSTEM WITH A LINE EQUILIBRIUM
Li Ch., Spott J.C., Thio W.
Received: October 26, 2013
A hyperchaotic system with an infinite line of equilibrium points is described. A criterion is proposed for quantifying the hyperchaos, and the position in the three-dimensional parameter space where the hyperchaos is largest is determined. In the vicinity of this point, different dynamics are observed including periodicity, quasi-periodicity, chaos, and hyperchaos. Under some conditions, the system has a unique bistable behavior, characterized by a symmetric pair of coexisting limit cycles that undergo period doubling, forming a symmetric pair of strange attractors that merge into a single symmetric chaotic attractor that then becomes hyperchaotic. The system was implemented as an electronic circuit whose behavior confirms the numerical predictions.