Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with time delays

Udhayakumar, K.; Rihan, Fathalla A.; Rakkiyappan, R.; Cao, Jinde

doi:10.1016/j.neunet.2021.10.027

Cited by 51 publications

(15 citation statements)

References 43 publications

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“…In [50], the bipartite fixed-time synchronization problem for fractional-order signed neural networks with discontinuous activation is discussed. In which the Filippove multimap is used to convert the F-TS of the fractional-order general solution into the zero solution of the fractional-order differential inclusions.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…In which the Filippove multimap is used to convert the F-TS of the fractional-order general solution into the zero solution of the fractional-order differential inclusions. In our work [50], we state and illustrate the F-TS lemmas of the delayed discontinuous systems, where the results are derived by using the second meanvalue theorem for definite integrals [51] for the fractionalorder 0 < ρ < 1. In the present paper, we considers the improved fixed-time stability problem of generalized delayed FOSs by using well known Lemma 1 in [49] and the concept of Gamma functions.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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New Fixed-Time Stability Theorems for Delayed Fractional-Order Systems and Applications

et al. 2022

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This paper examines the problem of improved fixed-time stability for generalized delayed fractional-order systems (FOSs). As a first step, some stability conditions are presented in two theorems to verify fixed-time stability (F-TS) of FOSs by using Lyapunov stability theory and indefinite Lyapunov functionals, where the fractional-order derivative of the indefinite functions may not exist. Furthermore, the corresponding estimated settling time of FOSs is also provided. Second, the results are extended to study fractional-order neural networks (FONNs) with time-delays in fixed-time synchronization. Using the Dirac delta functions, we propose an explicit saturated impulsive controller to synchronize the master and slave systems. Moreover, by constructing suitable indefinite Lyapunov-Krasovskii functions (LKF), we derive algebraic conditions to guarantee the fixed-time synchronization of the addressed FONNs. The simulation results demonstrate the feasibility and efficacy of the proposed method.

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Section: Numerical Simulationsmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

New Fixed-Time Stability Theorems for Delayed Fractional-Order Systems and Applications

et al. 2022

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“…Shafiya and Nagamani [24] set up a finite-time passivity criteria of fractional-order delayed neural networks via Lyapunov function approach. In details, one can see [25][26][27][28]. Especially, delay-driven Hopf bifurcation plays a vital role in fractional-order dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Dynamics and Control Mechanism of a Fractional-Order Delayed Brusselator Chemical Reaction Model

Xu¹,

Mu²,

Liu³

et al. 2022

MATCH

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Building differential dynamical systems to describe the changing relationship among chemical components is a vital aspect in chemistry. In this present manuscript, we put forward a new fractional-order delayed Brusselator chemical reaction model. By virtue of contraction mapping principle, we investigate the existence and uniqueness of the solution of fractional-order delayed Brusselator chemical reaction model. With the aid of mathematical analysis technique, we consider the non-negativeness of the solution of the fractional-order delayed Brusselator chemical reaction model. Making use of the theory of fractional-order dynamical system, we explore the stability and Hopf bifurcation issue of the fractional-order delayed Brusselator chemical reaction model. By designing a reasonable controller, we have availably controlled the time of emergence of Hopf bifurcation of the fractional-order delayed Brusselator chemical reaction model. A sufficient criterion guaranteeing the stability and the onset of Hopf bifurcation of the fractional-order controlled delayed Brusselator chemical reaction model is set up. Computer simulations are implemented to validate the theoretical findings. The derived fruits of this manuscript have great theoretical significance in controlling the concentrations of chemical substances.

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“…Ke [25] proded into the Mittag-Leffler stability and asymptotic ω-periodicity of fractional-order delayed inertial neural networks. In details, one can see [26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis and Bifurcation Study on Fractional-Order Tri-Neuron Neural Networks Incorporating Delays

Yan

et al. 2022

Fractal Fract

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A single paragraph of about 200 words maximum. For research articles, abstracts should provide a pertinent overview of the work. We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: place the question addressed in a broad context and highlight the purpose of the study; (2) Methods: describe briefly the main methods or treatments applied; (3) Results: summarize the article’s main findings; (4) Conclusion: indicate the main conclusions or interpretations. The abstract should be an objective representation of the article, it must not contain results which are not presented and substantiated in the main text and should not exaggerate the main conclusions.

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Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with time delays

Cited by 51 publications

References 43 publications

New Fixed-Time Stability Theorems for Delayed Fractional-Order Systems and Applications

New Fixed-Time Stability Theorems for Delayed Fractional-Order Systems and Applications

Bifurcation Dynamics and Control Mechanism of a Fractional-Order Delayed Brusselator Chemical Reaction Model

Dynamic Analysis and Bifurcation Study on Fractional-Order Tri-Neuron Neural Networks Incorporating Delays

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