Chaos, coexisting attractors and chaos control in a nonlinear dissipative chemical oscillator

Adéchinan, Joseph Adébiyi; Kpomahou, Y. J. F.; Hinvi, L. A.; Miwadinou, C. H.

doi:10.1016/j.cjph.2022.03.052

Cited by 13 publications

(7 citation statements)

References 32 publications

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“…Figure 1 shows various MATLAB signal portraits of the 4-D hyperchaotic two-scroll dynamics (1) for the initial data z(0) � (0.8, 0.2, 0.4, 0.6) and parameter data (a, b, c, d) � (25,8,90,6).…”

Section: A New Hyperchaotic System With Two-scroll Attractormentioning

confidence: 99%

“…Due to the rapid advancement of chaos theory, chaotic and hyperchaotic systems are applicable in several engineering branches such as memristive circuits [1][2][3][4], chemical oscillators [5][6][7], information sensing systems [8][9][10], lasers [11,12], and communication systems [13][14][15][16]. Xiu et al [17] designed a 5-D hyperchaotic system with hardware circuit design developed from a memristive cellular neural network (CNN) and applied it to build a secure communication system.…”

Section: Introductionmentioning

confidence: 99%

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A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

Vaidyanathan

Sambas

Tlelo‐Cuautle

et al. 2022

Discrete Dynamics in Nature and Society

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With the swift advancement of chaos theory, the modeling, chaotic oscillations, and engineering applications of chaotic and hyperchaotic systems are important topics in research. In this research paper, we elucidate our findings of a new four-dimensional two-scroll hyperchaotic system having only two quadratic nonlinearities and carry out a detailed bifurcation study of the proposed dynamical model. Also, an electronic circuit has been constructed for the new system using MultiSim (Version 14). The implementation of the new 4-D hyperchaotic system in a field-programmable gate array (FPGA) is performed herein by applying two numerical methods, viz. Forward Euler Method and Trapezoidal Method. The experimental results show a good match with the simulated hyperchaotic attractors. We also provide details of the hardware resources used for an FPGA Basys 3 Xilinx Artix-7 XC7A35T-ICPG236C.

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Section: A New Hyperchaotic System With Two-scroll Attractormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

Vaidyanathan

Sambas

Tlelo‐Cuautle

et al. 2022

Discrete Dynamics in Nature and Society

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“…Remark 1. Of course, we can add the delayed feedback controller to the second or third equation of model (3). Whether this control method is feasible or not requires similar analysis as Section 3.…”

Section: Chaos Suppression Via Delayed Feedback Controllermentioning

confidence: 99%

“…Of course, we can add the delayed mixed controller which includes state feedback and parameter perturbation to the first or second equation of model (3). Whether this control method is feasible or not requires similar analysis as Section 4.…”

Section: Remarkmentioning

confidence: 99%

“…Chaos widely exists in many areas, such as astronomy, quantum mechanics, economy and finance, weather, climate, network science, thermodynamics, chemistry, probabilistic mathematics, fluid mechanics and so on [1][2][3][4][5][6][7]. The study indicates that chaos has a very important application value in power system protection, flow dynamics, biomedicine, computer technique, information science, cryptology, communication engineering and so on [8].…”

Section: Introductionmentioning

confidence: 97%

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Chaos Suppression of a Fractional-Order Modificatory Hybrid Optical Model via Two Different Control Techniques

Gao

et al. 2022

Fractal Fract

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In this current manuscript, we study a fractional-order modificatory hybrid optical model (FOMHO model). Experiments manifest that under appropriate parameter conditions, the fractional-order modificatory hybrid optical model will generate chaotic behavior. In order to eliminate the chaotic phenomenon of the (FOMHO model), we devise two different control techniques. First of all, a suitable delayed feedback controller is designed to control chaos in the (FOMHO model). A sufficient condition ensuring the stability and the occurrence of Hopf bifurcation of the fractional-order controlled modificatory hybrid optical model is set up. Next, a suitable delayed mixed controller which includes state feedback and parameter perturbation is designed to suppress chaos in the (FOMHO model). A sufficient criterion guaranteeing the stability and the onset of Hopf bifurcation of the fractional-order controlled modificatory hybrid optical model is derived. In the end, software simulations are implemented to verify the accuracy of the devised controllers. The acquired results of this manuscript are completely new and have extremely vital significance in suppressing chaos in physics. Furthermore, the exploration idea can also be utilized to control chaos in many other differential chaotic dynamical models.

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Sinusoidal control strategy applied to continuous stirred‐tank reactors: Asymptotic and exponential convergence

Aguilar‐López,

González‐Viveros,

López‐Pérez

2024

Can J Chem Eng

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The main goal of this proposal is to present a class of nonlinear controllers for regulation and set point changes in continuous chemical reactors. The proposed control law has in its mathematical structure a proportional term of the regulation error to provide closed‐loop stability and a sinusoidal term, which can compensate for the nonlinearities of the plant. The closed‐loop stability of the plant is demonstrated via Lyapunov analysis, which reveals an asymptotic convergence of the control output to the required set points. Furthermore, the analysis of the regulation error's dynamic under the considered assumptions leads us to conclude that exponential stability is also reached. The controller is implemented via numerical experiments in two examples to generalize the applicability of the proposed approach by considering continuous stirred‐tank reactors models. The first case considers autocatalytic chemical oscillatory reactions that induce chaotic behaviour. For the second case, a process of acetone, butanol, and ethanol (ABE) fermentation through Clostridium acetobutylicum is considered. The proposed strategy shows an adequate performance because it can reach the required set point without long time settings and overshoot. A comparison with a smooth sliding‐mode and a standard proportional‐integral (PI) controller indicates the advantages of the proposed control approach.

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Chaos, coexisting attractors and chaos control in a nonlinear dissipative chemical oscillator

Cited by 13 publications

References 32 publications

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

Chaos Suppression of a Fractional-Order Modificatory Hybrid Optical Model via Two Different Control Techniques

Sinusoidal control strategy applied to continuous stirred‐tank reactors: Asymptotic and exponential convergence

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