Neimark–Sacker Bifurcation Analysis and 0–1 Chaos Test of an Interactions Model between Industrial Production and Environmental Quality in a Closed Area

Xin, Baogui; Wu, Zhi Fen

doi:10.3390/su70810191

Cited by 16 publications

(8 citation statements)

References 24 publications

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“…The 0 − 1 test algorithm (Gottwald and Melbourne 2004;Xin and Li 2013;Xin and Wu 2015) returns a real number K ∈ [0, 1] and a graph in 2D new coordinates (u, v)-plane.…”

Section: -1 Test Algorithm For Chaosmentioning

confidence: 99%

Bifurcation Analysis and 0-1 Chaos Test of a Discrete T System

Rana

2023

Chaos Theory and Applications

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This study examines discrete-time T system. We begin by listing the topological divisions of the system's fixed points. Then, we analytically demonstrate that a discrete T system sits at the foundation of a Neimark Sacker(NS) bifurcation under specific parametric circumstances. With the use of the explicit Flip-NS bifurcation criterion, we establish the flip-NS bifurcation's reality. Center manifold theory is then used to establish the direction of both bifurcations. We do numerical simulations to validate our theoretical findings. Additionally, we employ the $0-1$ test for chaos to demonstrate whether or not chaos exists in the system. In order to stop the system's chaotic trajectory, we ultimately employ a hybrid control method.

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“…The 0 − 1 test algorithm (Gottwald and Melbourne 2004;Xin and Li 2013;Xin and Wu 2015) returns a real number K ∈ [0, 1] and a graph in 2D new coordinates (u, v)-plane.…”

Section: -1 Test Algorithm For Chaosmentioning

confidence: 99%

Bifurcation Analysis and 0-1 Chaos Test of a Discrete T System

Rana

2023

Chaos Theory and Applications

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“…In this section, we are in a position to use the center manifold theorem and bifurcation theory to analyze in detail the local bifurcation problems of the system (1.3) at the fixed points E 1 , E 2 and E 3 , respectively. For related work, refer to [20][21][22][23][24][25].…”

Section: Bifurcation Analysismentioning

confidence: 99%

Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System

Liu

2022

Qual. Theory Dyn. Syst.

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After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system.Although the corresponding results for the equilibrium E 3 have been presented in a known literature, our results are more complete. The other is, what's more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria E 1 , E 2 and E 3 to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics -chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations.

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“…Zachilas et al briefly discussed about the implementation of 0-1 test on Hamiltonian systems they presented four Hamiltonian system two even and two odd order 40 and their results were matched with 0-1 test. Baogui Xin et al presented a discrete complex interaction model about industrial production and environmental quality in a closed area and then applied 0-1 test in order to validate the chaotic phenomenon of their model 41 . A simple method of detection chaos tool was presented by Daniel et al by combining the several such tool of detecting chaos mainly 0-1 test and presented it implementation heart rate variability 42 .…”

Section: Literature Reviewmentioning

confidence: 99%

Application of 0-1 test for chaos on forward converter to study the nonlinear dynamics

Ali

Iqbal

Muqeet³

et al. 2022

Sci Rep

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DC–DC converters has significant role in the applied power electronic systems, distributed power systems, computers, home appliances and communication equipment. A converter must remain within the specified range of operation. The main goal of this paper is to discuss the nonlinear behavior of forward converter and highlighted the application of the 0-1 test by applying it on the forward converter. As forward converter may contains electronic components, which cause instability in the system. So, it is necessary to understand its behavior when specifications of components are changed. To study chaotic behavior, 0-1 test will be applied on the forward converter, which is a novel technique outperform in unearthing the subtle chaotic behavior in deterministic dynamical systems. The forward converter goes from period-1, period-2, period-4 and finally become chaotic when the load resistance is varied. This variation in the behavior of the forward converter are analysis through 0-1 test for chaos. Moreover, time series plot, phase portrait and Bifurcation diagram for forward converter is also drawn for the validation of results obtained from 0-1 test. Test algorithm is applied via MATLAB and simulation of forward converter via MultiSim by varying its load resistance.

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Neimark–Sacker Bifurcation Analysis and 0–1 Chaos Test of an Interactions Model between Industrial Production and Environmental Quality in a Closed Area

Cited by 16 publications

References 24 publications

Bifurcation Analysis and 0-1 Chaos Test of a Discrete T System

Bifurcation Analysis and 0-1 Chaos Test of a Discrete T System

Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System

Application of 0-1 test for chaos on forward converter to study the nonlinear dynamics

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