Self-excited and hidden attractors in a novel chaotic system with complicated multistability

. In this paper, a new 3D chaotic system with trigonometric function term as a nonlinear controller is proposed. Depending on the nonlinear controller and the value of the parameters, the proposed system exhibits self-excited attractor with an unstable equilibrium, and hidden attractor with no equil...

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Bibliographic Details
Published in:European physical journal plus 2018-12, Vol.133 (12), p.557, Article 557
Main Authors: Natiq, Hayder, Said, M. R. M., Ariffin, M. R. K., He, Shaobo, Rondoni, Lamberto, Banerjee, Santo
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Atomic
Attractors (mathematics)
Chaos theory
Complex Systems
Condensed Matter Physics
Controllers
Cryptography
Equilibrium
Liapunov exponents
Mathematical and Computational Physics
Molecular
Nonlinear control
Optical and Plasma Physics
Parameter sensitivity
Physics
Physics and Astronomy
Pseudorandom
Random numbers
Regular Article
Statistical tests
Theoretical
Trigonometric functions
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Summary:. In this paper, a new 3D chaotic system with trigonometric function term as a nonlinear controller is proposed. Depending on the nonlinear controller and the value of the parameters, the proposed system exhibits self-excited attractor with an unstable equilibrium, and hidden attractor with no equilibrium or a stable equilibrium. In addition, the unusual and striking dynamic behavior of the coexistence of self-excited chaotic with periodic attractors, two self-excited chaotic attractors with periodic attractor, three periodic attractors, hidden chaotic with point attractors, two hidden chaotic attractors, and four hidden chaotic attractors are explored by selecting appropriate initial values. Consequently, the proposed system has high sensitivity to its initial values and parameters, hence it can be applied in chaos-based cryptographic applications. Thus, the non-periodicity of coexisting attractors of the system is investigated through Lyapunov exponents and Sample Entropy. To demonstrate the performance of the system in real applications, we construct a pseudo-random number generator (PRNG) based on the hidden attractor case. The randomness test results show that the generated PRNG pass all the statistical tests.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/i2018-12360-y