Bistable Hidden Attractors in a Novel Chaotic System with Hyperbolic Sine Equilibrium

Pham, Viet–Thanh; Volos, Christos; Kingni, Sifeu Takougang; Kapitaniak, Tomasz; Jafari, Sajad

doi:10.1007/s00034-017-0611-9

Cited by 37 publications

(16 citation statements)

References 70 publications

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“…Multistability, the result of coexistence of many kinds of nonlinear attractors, is the inherent property of many nonlinear dynamic systems. In recent years, it has become a very important research topic and has attracted much attention [41][42][43][44][45][46][47][48][49][50]. Multistability is rich in the diversity of stable states of nonlinear dynamic systems, which makes the system flexible.…”

Section: Multistability Analysismentioning

confidence: 99%

“…Multistability is one of the most important phenomena in dynamic systems [41][42][43][44][45][46][47][48][49][50], which occurs in many fields such as physics, biology, chemistry, economics, and electronics. Multistability allows flexibility of system performance without changing parameters, and appropriate control strategies can be used to induce switching behavior between different coexisting states [41].…”

Section: Introductionmentioning

confidence: 99%

“…Multistability allows flexibility of system performance without changing parameters, and appropriate control strategies can be used to induce switching behavior between different coexisting states [41]. For chaotic systems, hidden attractors [42][43][44][45][46] and infinite attractors [47][48][49][50] can exhibit multistability. For example, complex dynamic behaviors of coexisting attractors [51], transient chaos [52], and limit cycle [53] can be observed from hidden attractors.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Secure Communication Scheme Based on a New 5D Multistable Four-Wing Memristive Hyperchaotic System with Disturbance Inputs

Zhang

Liu

et al. 2020

Complexity

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By introducing a flux-controlled memristor model with absolute value function, a 5D multistable four-wing memristive hyperchaotic system (FWMHS) with linear equilibrium points is proposed in this paper. The dynamic characteristics of the system are studied in terms of equilibrium point, perpetual point, bifurcation diagram, Lyapunov exponential spectrum, phase portraits, and spectral entropy. This system is of the group of systems that have coexisting attractors. In addition, the circuit implementation scheme is also proposed. Then, a secure communication scheme based on the proposed 5D multistable FWMHS with disturbance inputs is designed. Based on parametric modulation theory and Lyapunov stability theory, synchronization and secure communication between the transmitter and receiver are realized and two message signals are recovered by a convenient robust high-order sliding mode adaptive controller. Through the proposed adaptive controller, the unknown parameters can be identified accurately, the gain of the receiver system can be adjusted continuously, and the disturbance inputs of the transmitter and receiver can be suppressed effectively. Thereafter, the convergence of the proposed scheme is proven by means of an appropriate Lyapunov functional and the effectiveness of the theoretical results is testified via numerical simulations.

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Section: Multistability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Secure Communication Scheme Based on a New 5D Multistable Four-Wing Memristive Hyperchaotic System with Disturbance Inputs

Zhang

Liu

et al. 2020

Complexity

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“…Compared with traditional schemes, chaotic information encryption technology is suggested to have higher security and rapidity [3], [4]. The complex dynamic behavior of chaotic systems is of great importance to the security in chaotic encryption communication system [5]- [8]. It is generally known that the running time will increase significantly when discretizing a continuous chaotic system.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Optimization Control of a Robust Chaotic Map

Qian

et al. 2019

IEEE Access

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Robust chaos in the discrete system is suggested to have practical as well as theoretical importance since it can obtain reliable operation in the chaotic mode. However, it receives only moderate attention and only focuses on a finite chaotic parameter space and small Lyapunov exponents. This paper introduces a two-dimensional smooth map and studies its robustness of chaos in the infinite parameter space. Then, a compound operation-based optimization control method is introduced to increase the map complexity in the measure of Lyapunov exponent. The introduced method is simple and provides a new pathway for exploring the robustness and complexity of discrete chaotic system. Finally, we design a chaosbased pseudo-random number generator (CPNG) based on the optimized robust chaotic map, and the careful analysis shows that the proposed CPNG has high quality of randomness and has passed the rigorous National Institute of Standards and Technology (NIST) test.

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“…Many scientists have studied the modelling of chaotic systems having special types of equilibrium curves such as line equilibrium [14,15], circle [16], hyperbola [17], parabola [18], cloud-shaped curve [19], rectangle [20], ellipse [20], square [21], hyperbolic sine curve [22], hyperbolic tangent curve [23], exponential curve [24], heart-shaped curve [25], conic-shaped curve [26], axe-shaped curve [27], conchshaped curve [28] etc.…”

Section: Introductionmentioning

confidence: 99%

A New Chaotic System with a Pear-shaped Equilibrium and its Circuit Simulation

Sambas¹,

Vaidyanathan

Mamat

et al. 2018

IJECE

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This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility.

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Bistable Hidden Attractors in a Novel Chaotic System with Hyperbolic Sine Equilibrium

Cited by 37 publications

References 70 publications

Secure Communication Scheme Based on a New 5D Multistable Four-Wing Memristive Hyperchaotic System with Disturbance Inputs

Secure Communication Scheme Based on a New 5D Multistable Four-Wing Memristive Hyperchaotic System with Disturbance Inputs

Dynamics and Optimization Control of a Robust Chaotic Map

A New Chaotic System with a Pear-shaped Equilibrium and its Circuit Simulation

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