A chaos control strategy for the fractional 3D Lotka–Volterra like attractor

Naik, Manisha Krishna; Baishya, Chandrali; Veeresha, P.

doi:10.1016/j.matcom.2023.04.001

Cited by 17 publications

(4 citation statements)

References 48 publications

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“…It is noteworthy that richer dynamic phenomena have been found in fractional-order nonlinear systems, such as limit cycle [17], bifurcation [18], resonance [19] and synchronization [20]. Interestingly, chaotic behavior has also been discovered in some fractional-order dynamical systems, such as the fractional-order Rösslor system [21], the fractional-order Duffing system [22], the fractional-order Lorenz system [23], the fractional-order Liu system [24] and so on [25][26][27][28]. It should be mentioned that these systems have many remarkable properties, including extreme sensitivity to initial conditions, unpredictability, internal randomness and ergodicity.…”

Section: Introductionmentioning

confidence: 99%

A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

Tang,

Li,

Huang

2024

Phys. Scr.

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A novel 4D fractional-order chaotic entanglement system based on sinusoidal functions is established in this paper. We aim to reveal the relationship between the dynamical behavior of the new system and its entanglement coefficients. It is found that the equilibrium point of the system varies regularly with the successive change of the entanglement coefficient. The supercritical pitchfork bifurcation phenomenon of the new system is discussed based on the fractional-order stability theory. Furthermore, sufficient conditions and threshold for supercritical Hopf bifurcation caused by the entanglement coefficient are provided. Finally, the route to chaos of the new system is explored utilizing multiple numerical indicators, such as spectral entropy complexity, bifurcation diagrams, Lyapunov exponential spectrum, phase portraits, and 0-1 test curves. The results indicate that in addition to various chaotic attractors, there are phenomena such as period-doubling bifurcations, period windows, and coexisting symmetric attractors (periodic or chaotic).

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Section: Introductionmentioning

confidence: 99%

A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

Tang,

Li,

Huang

2024

Phys. Scr.

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“…Mathematical models given by ordinary differential equations (ODEs) [1,2] are used to describe the time evolution of dynamical systems in many branches of science. The ODEs model different dynamical phenomena that originate from mechanical engineering [3][4][5], neuroscience [6,7], physics [8][9][10][11], medicine [12,13], electromechanics [14,15], production technologies [16,17], ecology [18,19], biology [20][21][22][23], climate dynamics [24,25], and many more. Still, every case may require a different approach for dynamical analysis.…”

Section: Introductionmentioning

confidence: 99%

A Unified Approach for the Calculation of Different Sample-Based Measures with the Single Sampling Method

Leszczynski,

Perlikowski,

Brzeski

2024

Mathematics

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This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase space structure, and system dynamics predictability. Basin stability assesses the overall likelihood of reaching specific solutions, while the basin entropy measure aims to capture the structure of attraction basins and the complexity of their boundaries. Although these two metrics complement each other effectively, their original procedures for computation differ significantly. This paper introduces a universal approach and algorithm for calculating basin stability and entropy measures. The suitability of these procedures is demonstrated through the analysis of two non-linear systems.

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“…Eshaghi et al [29] discussed the bifurcation, synchronization, and chaos control of a fractional-order chaotic system. For more details, one can see [29,[34][35][36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Exploring Dynamics and Hopf Bifurcation of a Fractional-Order Bertrand Duopoly Game Model Incorporating Both Nonidentical Time Delays

et al. 2023

Fractal Fract

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In order to maximize benefits, oligopolistic competition often occurs in contemporary society. Establishing the mathematical models to reveal the law of market competition has become a vital topic. In the current study, on the basis of the earlier publications, we propose a new fractional-order Bertrand duopoly game model incorporating both nonidentical time delays. The dynamics involving existence and uniqueness, non-negativeness, and boundedness of solution to the considered fractional-order Bertrand duopoly game model are systematacially analyzed via the Banach fixed point theorem, mathematical analysis technique, and construction of an appropriate function. Making use of different delays as bifurcation parameters, several sets of new stability and bifurcation conditions ensuring the stability and the creation of Hopf bifurcation of the established fractional-order Bertrand duopoly game model are acquired. By virtue of a proper definite function, we set up a new sufficient condition that ensures globally asymptotically stability of the considered fractional-order Bertrand duopoly game model. The work reveals the impact of different types of delays on the stability and Hopf bifurcation of the proposed fractional-order Bertrand duopoly game model. The study shows that we can adjust the delay to achieve price balance of different products. To confirm the validity of the derived criteria, we put computer simulation into effect. The derived conclusions in this article are wholly new and have great theoretical value in administering companies.

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A chaos control strategy for the fractional 3D Lotka–Volterra like attractor

Cited by 17 publications

References 48 publications

A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

A Unified Approach for the Calculation of Different Sample-Based Measures with the Single Sampling Method

Exploring Dynamics and Hopf Bifurcation of a Fractional-Order Bertrand Duopoly Game Model Incorporating Both Nonidentical Time Delays

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