A complete analytical study on the dynamics of simple chaotic systems
- 6 Downloads
We report, in this paper, a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical solutions revealing several chaotic phenomena such as antimonotonicity, period-doubling sequences and Feignbaum remerging have been presented. Further, the analytical solutions are used to obtain basins of attraction, phase portraits and Poincare maps for different chaotic systems. Experimentally observed chaotic attractors in some of the systems are presented to confirm the analytical results. The bifurcations and chaotic phenomena studied through explicit analytical solutions are reported in the literature for the first time.
KeywordsChaos antimonotonicity piecewise linear
PACS Nos05.45.−a 05.45.Ac
One of the authors A Arulgnanam gratefully acknowledges Dr K Thamilmaran, the Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirapalli, for his help and permission to carry out the experimental work during his doctoral programme.
- 2.M Lakshmanan and K Murali, Curr. Sci. 67, 989 (1994)Google Scholar
- 3.M Lakshmanan and S Rajasekar, Nonlinear dynamics: Integrability, chaos and patterns (Springer, Berlin, 2003)Google Scholar
- 4.T Matsumoto, IEEE Trans. Circuits Syst. 31, 1055 (1984)Google Scholar
- 5.K Murali, M Lakshmanan and L O Chua, IEEE Trans. Circuits Syst. 41, 462 (1994)Google Scholar
- 8.A Arulgnanam, K Thamilmaran and M Daniel, Chin. J. Phys. 53, 060702 (2015)Google Scholar
- 13.M Lakshmanan and K Murali, Phil. Trans: Phys. Sci. Eng. 353, 1701 (1995)Google Scholar