Cosine chaotification technique to enhance chaos and complexity of discrete systems

Abstract We hereby propose a cosine chaotification technique (CCT), which has simple structure, complex nonlinear dynamics and bounded orbits, to enhance the chaotic behavior as well as the complexity performance of discrete chaotic systems. To demonstrate the effectiveness of the CCT, we apply the CCT on three different examples, including one-dimensional (1D) logistic map, two population chaotic maps, and the three-dimensional (3D) Hénon map. Performance evaluations prove that the CCT can change the chaotic and non-chaotic states of these maps to chaotic or hyperchaotic state with higher complexity performance. Besides that, the generated maps by CCT have wider chaotic and hyperchaotic behaviors than the existing chaotic maps.

[1]  Lamberto Rondoni,et al.  Self-excited and hidden attractors in a novel chaotic system with complicated multistability , 2018, The European Physical Journal Plus.

[2]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[3]  S. Palit,et al.  Optical complexity in external cavity semiconductor laser , 2017 .

[4]  Yicong Zhou,et al.  2D Sine Logistic modulation map for image encryption , 2015, Inf. Sci..

[5]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Weiting Chen,et al.  Measuring complexity using FuzzyEn, ApEn, and SampEn. , 2009, Medical engineering & physics.

[7]  Yicong Zhou,et al.  Sine-Transform-Based Chaotic System With FPGA Implementation , 2018, IEEE Transactions on Industrial Electronics.

[8]  Hayder Natiq,et al.  Can hyperchaotic maps with high complexity produce multistability? , 2019, Chaos.

[9]  Sayan Mukherjee,et al.  Complexity in congestive heart failure: A time-frequency approach. , 2016, Chaos.

[10]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[11]  Adem Kiliçman,et al.  Dynamics and Complexity of a New 4D Chaotic Laser System , 2019, Entropy.

[12]  Yicong Zhou,et al.  Dynamic Parameter-Control Chaotic System , 2016, IEEE Transactions on Cybernetics.

[13]  O. Rössler.  An equation for continuous chaos , 1976 .

[14]  Guanrong Chen,et al.  Single-Input Multi-Output State-Feedback Chaotification of General Discrete Systems , 2004, Int. J. Bifurc. Chaos.

[15]  Guanrong Chen,et al.  Introduction to anti-control of discrete chaos: theory and applications , 2006, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[16]  G. Baier,et al.  Maximum hyperchaos in generalized Hénon maps , 1990 .

[17]  Kehui Sun,et al.  Dynamical properties and complexity in fractional-order diffusionless Lorenz system , 2016 .

[18]  Hayder Natiq,et al.  A new hyperchaotic map and its application for image encryption , 2018, The European Physical Journal Plus.

[19]  Firdaus E. Udwadia,et al.  An efficient QR based method for the computation of Lyapunov exponents , 1997 .

[20]  Shaobo He,et al.  Multicavity formations and complexity modulation in a hyperchaotic discrete system , 2018 .

[21]  Jun Wang,et al.  Chaotic Time Series Prediction Based on a Novel Robust Echo State Network , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Jiangping Hu,et al.  Chaotification of a class of linear switching systems based on a Shilnikov criterion , 2017, J. Frankl. Inst..

[23]  Adem Kilicman,et al.  Designing an M-dimensional nonlinear model for producing hyperchaos , 2018, Chaos, Solitons & Fractals.

[24]  J. Kurths,et al.  Generalized variable projective synchronization of time delayed systems. , 2013, Chaos.

[25]  Guanrong Chen,et al.  On the security defects of an image encryption scheme , 2009, Image Vis. Comput..

[26]  Yicong Zhou,et al.  Cascade Chaotic System With Applications , 2015, IEEE Transactions on Cybernetics.

[27]  F. R. Marotto.  The dynamics of a discrete population model with threshold , 1982 .

[28]  J. Sprott,et al.  Some simple chaotic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  Minfen Shen,et al.  Convergence Analysis for Initial Condition Estimation in Coupled Map Lattice Systems , 2012, IEEE Transactions on Signal Processing.