, 92:42 | Cite as

A complete analytical study on the dynamics of simple chaotic systems

  • G Sivaganesh
  • A ArulgnanamEmail author
  • A N Seethalakshmi


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.


Chaos antimonotonicity piecewise linear 


05.45.−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.


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Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of PhysicsAlagappa Chettiar Government College of Engineering and TechnologyKaraikudiIndia
  2. 2.Department of Physics, St. John’s College (affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli 627 012, India)PalayamkottaiIndia
  3. 3.Department of Physics, The M.D.T. Hindu College (affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli 627 012, India)TirunelveliIndia

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