A new five-term simple chaotic attractor. (English) Zbl 1234.37030

Summary: A new chaotic attractor is presented with only five terms in three simple differential equations having fewer terms and simpler than those of existing seven-term or six-term chaotic attractors. Basic dynamical properties of the new attractor are demonstrated in terms of equilibria, Jacobian matrices, non-generalized Lorenz systems, Lyapunov exponents, a dissipative system, a chaotic waveform in time domain, a continuous frequency spectrum, Poincaré maps, bifurcations and forming mechanisms of its compound structures.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37J20 Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems
37M05 Simulation of dynamical systems
68U20 Simulation (MSC2010)
Full Text: DOI


[1] Lorenz, E.N., J. atmos. sci., 20, 130, (1963)
[2] Rössler, O.E., Phys. lett. A, 57, 5, 397, (1976)
[3] Chen, G.; Ueta, T., Int. J. bifur. chaos, 9, 7, 1465, (1999)
[4] Lü, J.; Chen, G., Int. J. bifur. chaos, 12, 3, 659, (2002)
[5] Liu, C.; Liu, T.; Liu, L.; Liu, K., Chaos solitons fractals, 22, 1031, (2004)
[6] Zhou, W.; Xu, Y.; Lu, H.; Pan, L., Phys. lett. A, 372, 5773, (2008) · Zbl 1223.37045
[7] Sprott, J.C., Phys. rev. E, 50, 2, R647, (1994)
[8] Sprott, J.C., Phys. lett. A, 228, 271, (1997)
[9] Toncharoen, C.; Srisuchinwong, B., Ecti-con, 2009, 1, 407, (2009)
[10] Ueta, T.; Chen, G., Int. J. bifur. chaos, 10, 1917, (2000)
[11] Wang, X.F.; Chen, G., Int. J. bifur. chaos, 10, 549, (2000)
[12] Celikovsky, S.; Chen, G., Chaos solitons fractals, 26, 1271, (2005)
[13] Wolf, A.; Swift, J.B.; Swinney, H.L.; Vastano, J.A., Physica D, 16, 285, (1985)
[14] Lu, J.; Chen, G.; Zhang, S., Chaos solitons fractals, 14, 669, (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.