Simulation and experimental validation of a non-equilibrium chaotic system

Jahanshahi, Hadi; Orozco-López, Onofre; Muñoz‐Pacheco, Jesús M.; Alotaibi, Naif D.; Volos, Christos; Wang, Zhen; Sevilla-Escoboza, R.; Chu, Yu‐Ming

doi:10.1016/j.chaos.2020.110539

Cited by 59 publications

(11 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Multi-stability [16][17][18] means the coexistence of multiple attractors, which is an inherent characteristic of many nonlinear dynamical systems. Concurrently, multi-stability can be applied in image processing or as a random source for information engineering applications.…”

Section: Hidden Coexisting Attractorsmentioning

confidence: 99%

“…That same year, Deng et al presented four-wing hidden attractors with one stable equilibrium point [17]. In 2021, Jahanshahi et al discussed a four-dimensional system with hidden attractors that lacks equilibria [18]. Gu et al also discovered a novel non-equilibrium memristor-based system with multi-wing attractors and multiple transient transitions [19].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generating novel multi-scroll chaotic attractors via fractal transformation

et al. 2022

View full text Add to dashboard Cite

The fractal and chaos are bound tightly, and their relevant researches are well-established. Few of them, however, concentrates on the research of the possibility of combining the fractal and the chaotic systems to generate multi-scroll chaotic attractors. This paper presents a novel non-equilibrium point chaotic system, exhibiting extremely rich and complex hidden behaviors including chaos, hyper-chaos, multiscroll attractors, extreme multi-stability and initial offset-boosting. The proposed system is combined with fractal transformation respectively, and a new class of multi-scroll attractors, such as multi-ring attractors and separated-scroll attractors, is observed. Particularly, swallow-shaped attractors for the first time is found. Moreover, another efficient method to generate a different class of chaotic attractors uses parabola transformation and triangle transformation. Additionally, the spectrum entropy (SE) complexity is employed to discuss the complexity of the proposed system before and after fractal, resulting in a chaotic sequences with fractal transformation that has higher complexity. Finally, we develop a hardware platform to implement the presented attractors before and after fractal in a way to confirm the accuracy of the numerical simulations, providing a theoretical basis for the next application in image encryption.

show abstract

Section: Hidden Coexisting Attractorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generating novel multi-scroll chaotic attractors via fractal transformation

et al. 2022

View full text Add to dashboard Cite

show abstract

“…In recent years, the hidden attractor [62][63][64][65][66][67][68][69][70][71][72][73][74][75][76], as a special class of newly defined attractor, has attracted extensive attention from researchers. e attractor that we usually say is also called the self-excited attractor, which is caused by the unstable equilibrium.…”

Section: Multistability and Coexisting Multiple Attractorsmentioning

confidence: 99%

Recent Advances in Dimensionality Reduction Modeling and Multistability Reconstitution of Memristive Circuit

2021

View full text Add to dashboard Cite

Due to the introduction of memristors, the memristor-based nonlinear oscillator circuits readily present the state initial-dependent multistability (or extreme multistability), i.e., coexisting multiple attractors (or coexisting infinitely many attractors). The dimensionality reduction modeling for a memristive circuit is carried out to realize accurate prediction, quantitative analysis, and physical control of its multistability, which has become one of the hottest research topics in the field of information science. Based on these considerations, this paper briefly reviews the specific multistability phenomenon generating from the memristive circuit in the voltage-current domain and expounds the multistability control strategy. Then, this paper introduces the accurate flux-charge constitutive relation of memristors. Afterwards, the dimensionality reduction modeling method of the memristive circuits, i.e., the incremental flux-charge analysis method, is emphatically introduced, whose core idea is to implement the explicit expressions of the initial conditions in the flux-charge model and to discuss the feasibility and effectiveness of the multistability reconstitution of the memristive circuits using their flux-charge models. Furthermore, the incremental integral transformation method for modeling of the memristive system is reviewed by following the idea of the incremental flux-charge analysis method. The theory and application promotion of the dimensionality reduction modeling and multistability reconstitution are proceeded, and the application prospect is prospected by taking the synchronization application of the memristor-coupled system as an example.

show abstract

“…Also, in the current study, a new variable fractionalorder network is proposed for modeling of hepatitis B. By studying the factional order [45][46][47][48][49][50][51][52][53][54][55][56] or variable fractional-order network, we aim to consider the impact of the interaction between different communities on the disease rate in different societies. The relationships and travels between two countries, for instance, will definitely affect the rate of diseases in both of them.…”

Section: Introductionmentioning

confidence: 99%

Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network

Din

Yusuf

et al. 2022

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

This paper aims at analyzing the dynamical behavior of a SIR hepatitis B epidemic stochastic model via a novel approach by incorporating the effect of information interventions and random perturbations. Initially, we demonstrate the positivity and global existence of the solutions. Afterward, we derive the stochastic threshold parameter Rs, followed by the fact that this number concludes the transmission of hepatitis B from the population. By increasing the intensity of noise, we get Rs less than one, inferring that ultimately hepatitis B will lapse. While decreasing the intensity of noise to a sufficient level, we have Rs > 1. For the case Rs > 1, adequate results for the presence of stationary distribution are achieved, showing the prevalence of hepatitis B. The present study also involves the derivation of the necessary conditions for the persistence of the epidemic. Finally, the main theoretical solutions are plotted through simulations. Discussion on theoretical and numerical results shows that utilizing random perturbations and information interventions have a pronounced impact on the syndrome's dynamics. Furthermore, since most communities interact with each other, and the disease spread rate is affected by this factor, a new variable-order fractional network of the stochastic hepatitis B model is offered. Subsequently, this study will provide a robust theoretical basis for comprehending worldwide SIR stochastic and variable-order fractional network-related case studies.

show abstract

Simulation and experimental validation of a non-equilibrium chaotic system

Cited by 59 publications

References 50 publications

Generating novel multi-scroll chaotic attractors via fractal transformation

Generating novel multi-scroll chaotic attractors via fractal transformation

Recent Advances in Dimensionality Reduction Modeling and Multistability Reconstitution of Memristive Circuit

Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network

Contact Info

Product

Resources

About