Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 18, Issue 11, Pages 3309-3324Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127408022391
Keywords
Chaos; hyperchaos; center manifold; pitchfork bifurcation; Lyapunov exponent
Funding
- National Natural Science Foundation of China [60774088, 60574036]
- Special Research Funds for the Doctoral Program of Higher Education of China [20050055013]
- Program for New Century Excellent Talents in Universities of China (NCET)
- Science & Technology Research Key Project of Education Ministry of China [107024]
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This paper is concerned with a novel four-dimensional continuous autonomous hyperchaotic system, which is obtained by adding a simple dynamical state-feedback controller to a Lorenzlike three-dimensional autonomous chaotic system. This new system contains three parameters and each equation of the system has one quadratic cross-product term. Some basic properties of the system are studied first. Its complex dynamic behaviors are then analyzed by means of Lyapunov exponent (LE) spectrum, bifurcation diagrams, phase portraits and Poincare sections. It is shown that the system has several large hyperchaotic regions. When the system is evolving in a hyperchaotic region, the two positive LEs are both large, which can be larger than 1 if the system parameters are taken appropriately. The pitchfork bifurcation of the system is finally analyzed by using the center manifold theorem.
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