Lower-dimensional simple chaotic systems with spectacular features

Wang, Zhen; Ahmadi, Atefeh; Tian, Huaigu; Jafari, Sajad; Chen, Guanrong

doi:10.1016/j.chaos.2023.113299

Cited by 49 publications

(14 citation statements)

References 109 publications

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“…For example, according to the number of coexisting attractors, some such systems can be classified into two specific cases: mega-stable and extreme multi-stable systems. This is shown, for example, by Wang et al [36] in their work entitled 'Lower-dimensional simple chaotic systems with spectacular features'. The importance of coexisting attractors is that it provides multiple optional steady states for the system to respond to different needs.…”

Section: Introductionmentioning

confidence: 77%

Nonlinear dynamics, coexistence of attractors and microcontroller implementation of a modified Helmholtz Jerk oscillator

Fangnon¹,

Tamba²,

Miwadinou

et al. 2023

Phys. Scr.

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In this work, we converted a two-dimensional modiﬁed Helmholtz oscillator into a three-dimensional modiﬁed Helmholtz jerk oscillator. The study of the stability of the ﬁxed points is made and by using the theorem of Hopf, the condition of existence of the bifurcation of Hopf is sought. By numerical simulations relating to the diagrams of the basin of parameters, attraction, bifurcation, the Lyapunov exponents and the phase portrait, the global dynamics as well as the coexistence of the attractors of the system are analyzed. This study revealed that the considered modiﬁed Jerk Helmholtz oscillator can generate Hopf bifurcation, bistable limit cycles, coexistence of chaotic and periodic attractors for appropriate choices of system parameter values. The microcontroller based implementation of the modiﬁed Jerk Helmholtz oscillator is proposed to experimentally verify the obtained analytical and numerical results. Finally, to control the amplitude of the Lyapunov attractor and exponent, we added two new parameters in the modiﬁed Helmholtz jerk oscillator.

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Section: Introductionmentioning

confidence: 77%

Nonlinear dynamics, coexistence of attractors and microcontroller implementation of a modified Helmholtz Jerk oscillator

Fangnon¹,

Tamba²,

Miwadinou

et al. 2023

Phys. Scr.

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“…Generally, the main indicators involved are GDP (Gross Domestic Product) growth rate, GDP deflator, exchange rate fluctuation, growth rate of money supply, financing amount of securities institutions, product price index, enterprise prosperity, non-performing loan ratio, asset liability ratio, provision coverage ratio, asset return ratio, interest protection multiple, etc. Table 1 shows the analysis of the impact of changes in various indicators on the risks of the energy finance industry (Zhang et al, 2019;Wang et al, 2023).…”

Section: Risk Warning Indicator Systemmentioning

confidence: 99%

Energy finance risk warning model based on GABP algorithm

Nai

2023

Front. Energy Res.

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Energy finance is the product of the close combination of the energy industry and the financial industry, and the two affect each other. The energy crisis may lead to a financial crisis, and the financial crisis may also lead to a energy crisis. Early risk warning for the energy financial crisis can effectively mitigate and reduce risks. This article used the GABP (Genetic Algorithm Back Propagation) algorithm model to systematically analyze and predict the risks of energy financial crises. After establishing indicators for energy finance risk warning, this article collected relevant data from 150 energy companies and 210 financial companies, and compared them with the GABP algorithm model and manual analysis model. The error value of the model is determined by the numerical expansion in the positive and negative directions based on zero scale values. The closer the zero scale value is, the smaller the error; the farther it is from the zero scale value, the greater the error. The results show that the average accuracy of the GABP model for energy finance risk warning is 85.2%, and the minimum error value is −0.23. The average accuracy of using manual analysis models for energy finance risk warning is 75.8%, with a minimum error value of 1.89. The GABP algorithm has advantages in constructing energy finance risk warning models.

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“…Chaotic behaviour can be observed in various systems, including mechanical devices, fluid dynamics, electrical circuits, artificial intelligence, neural networks, lasers, ecological population expansion, molecular vibration dynamics, and weather. The behaviour of chaotic systems [13][14][15] appears to be random since it is sensitive to the initial conditions, even if these systems are deterministic via some description by mathematical rules. One of the chaotic systems discovered by Genesio and Tesi, known as the chaotic Genesio-Tesi system (GTS) [12,16], it includes three ordinary differential equations with three positive real parameters.…”

Section: Introductionmentioning

confidence: 99%

Quasilinearization variational iteration method for system of nonlinear ODEs

Sinha,

Maroju

2024

Phys. Scr.

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In this manuscript, we discuss a new technique for solving system of nonlinear differential equations, which is a modification of the variation iteration method (VIM) implemented using the quasilinearization method and Adomian's polynomial. The quasilinearization variational iteration method (QVIM) is the name given to this proposed method. The proposed method's convergence analysis in Banach space is also discussed here. Three application problems, including the Genesio-Tesi system, are considered to test the applicability of our approach. We also discuss the case study of the chaotic and non-chaotic solutions of the Genesio-Tesi system (GTS). The convergence behaviour of the method is studied for various values of parameter x. To assess the viability and efficacy of QVIM, we compare it to the existing well-known Adomian decomposition method. The results show that the proposed method is highly efficient and simple to implement.

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Lower-dimensional simple chaotic systems with spectacular features

Cited by 49 publications

References 109 publications

Nonlinear dynamics, coexistence of attractors and microcontroller implementation of a modified Helmholtz Jerk oscillator

Nonlinear dynamics, coexistence of attractors and microcontroller implementation of a modified Helmholtz Jerk oscillator

Energy finance risk warning model based on GABP algorithm

Quasilinearization variational iteration method for system of nonlinear ODEs

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