CS  Vol.2 No.2 , April 2011
A New Chaotic Behavior from Lorenz and Rossler Systems and Its Electronic Circuit Implementation
ABSTRACT
This paper presents a new three-dimensional continuous autonomous chaotic system with ten terms and three quadratic nonlinearities. The new system contains five variational parameters and exhibits Lorenz and Rossler like attractors in numerical simulations. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures. Some of the basic dynamic behavior of the system is explored further investigation in the Lyapunov Exponent. The new system examined in Matlab-Simulink and Orcad-PSpice. An electronic circuit realization of the proposed system is presented using analog electronic elements such as capacitors, resistors, operational amplifiers and multipliers.

Cite this paper
nullQ. Alsafasfeh and M. Al-Arni, "A New Chaotic Behavior from Lorenz and Rossler Systems and Its Electronic Circuit Implementation," Circuits and Systems, Vol. 2 No. 2, 2011, pp. 101-105. doi: 10.4236/cs.2011.22015.
References
[1]   G. Chen and X. Dong, “From Chaos to Order: Methodologies, Perspectives and Applications,” World Scientific Publishing, Singapore, 1998. doi:10.1142/9789812798640

[2]   K. M. Cuomo, A. V. Op-penheim and S. H. Strogatz, “Synchronization of Lorenz-Based Chaotic Circuits with Applicationsto Communications,” IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, Vol. 40, No. 10, 1993, pp. 626-633. doi:10.1109/82.246163

[3]   E. N. Lorenz, “Deterministic Nonperiodic Flow,” Journal of Atmospheric Sciences, Vol. 20, No. 2, 1963, pp. 130-141. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2

[4]   O. E. Rossler, “An Equation for Continuous Chaos,” Physics Letters A, Vol. 57, No. 5, 1976, pp. 397-398. doi:10.1016/0375-9601(76)90101-8

[5]   W. Yu, J. Cao, K. Wong and J. Lu, “New Communication Schemes Based on Adaptive Synchronization,” Chaos, Vol. 17, No. 3, 2007, pp. 33-114.

[6]   J. H. Lü, G. Chen, D. Cheng and S. Celikovsky, “Bridge the Gap between the Lorenz System and the Chen Sys-tem,” International Journal of Bifurcation and Chaos, Vol. 12, No. 12, 2002, pp. 2917-2926.

[7]   S. Celikovsky and G. Chen, “On a Generalized Lorenz Canonical Form of Chaotic Systems,” International Journal of Bifurcation and Chaos, Vol. 12, No. 8, 2002, pp. 1789-1812. doi:10.1142/S0218127402005467

[8]   J. Lü, G. Chen and S. Zhang, “Dynamical Analysis of a New Chaotic Attractor,” International Journal of Bifurcation and Chaos, Vol. 12, No. 5, 2002, pp. 1001-1015.

[9]   S. Nakagawa and T. Saito, “An RC OTA Hysteresis Chaos Generator,” IEEE Transactions on Circuits Systems Part I: Fundamental Theory and Applications, Vol. 43, No. 12, 1996, pp. 1019-1021. doi:10.1109/81.545846

[10]   J. Lü and G. Chen, “Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications,” International Journal of Bifurcation and Chaos, Vol. 16, No. 4, 2006, pp. 775-858. doi:10.1142/S0218127406015179

[11]   M. E. Yalcin, J. A. K. Suykens, J. Vandewalle and S. Ozoguz, “Families of Scroll Grid Attractors,” International Journal of Bifurcation and Chaos, Vol. 12, No. 1, 2002, pp. 23-41. doi:10.1142/S0218127402004164

[12]   K. M. Cuomo and A. V. Oppenheim, “Circuit Implementation of Synchronized Chaos with Applications to Communications,” Physical Review Letters, Vol. 71, No. 65, 1993, pp. 65-68. doi:10.1103/PhysRevLett.71.65

 
 
Top