Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations

Stamov, Gani; Stamova, Ivanka; Venkov, George; Stamov, Trayan; Spirova, Cvetelina

doi:10.3390/math8071082

Cited by 14 publications

(6 citation statements)

References 51 publications

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“…Hence, the Lyapunov stability proof establishes that a dynamical system is asymptotically stable if there exists a definite Lyapunov function V(S), such that V: [93][94][95]. Thus, the Lyapunov function chosen is Equation (31); the correspondent time derivative is defined in Equation (32).…”

Section: Stability Proofmentioning

confidence: 99%

High-Performance Tracking for Piezoelectric Actuators Using Super-Twisting Algorithm Based on Artificial Neural Networks

et al. 2021

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Piezoelectric actuators (PEA) are frequently employed in applications where nano-Micr-odisplacement is required because of their high-precision performance. However, the positioning is affected substantially by the hysteresis which resembles in an nonlinear effect. In addition, hysteresis mathematical models own deficiencies that can influence on the reference following performance. The objective of this study was to enhance the tracking accuracy of a commercial PEA stack actuator with the implementation of a novel approach which consists in the use of a Super-Twisting Algorithm (STA) combined with artificial neural networks (ANN). A Lyapunov stability proof is bestowed to explain the theoretical solution. Experimental results of the proposed method were compared with a proportional-integral-derivative (PID) controller. The outcomes in a real PEA reported that the novel structure is stable as it was proved theoretically, and the experiments provided a significant error reduction in contrast with the PID.

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Section: Stability Proofmentioning

confidence: 99%

High-Performance Tracking for Piezoelectric Actuators Using Super-Twisting Algorithm Based on Artificial Neural Networks

et al. 2021

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“…For more results on the corresponding fundamental and qualitative dynamical behaviors of impulsive reaction-diffusion systems, we refer to [ 36 , 54 , 55 , 56 , 57 ]. The consideration of impulsive conditions allows us to take into account short-term effects on susceptible cells, infected cells, and free viruses.…”

Section: Model Description and Preliminariesmentioning

confidence: 99%

“…Next, we will define the class of Lyapunov-like functions [ 31 , 36 , 55 , 56 ] that will be used in the study of the qualitative properties of integral manifolds, related to the model (2).…”

Section: Model Description and Preliminariesmentioning

confidence: 99%

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Impulsive Reaction-Diffusion Delayed Models in Biology: Integral Manifolds Approach

Stamov

Stamova

Spirova

2021

Entropy

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In this paper we study an impulsive delayed reaction-diffusion model applied in biology. The introduced model generalizes existing reaction-diffusion delayed epidemic models to the impulsive case. The integral manifolds notion has been introduced to the model under consideration. This notion extends the single state notion and has important applications in the study of multi-stable systems. By means of an extension of the Lyapunov method integral manifolds’ existence, results are established. Based on the Lyapunov functions technique combined with a Poincarè-type inequality qualitative criteria related to boundedness, permanence, and stability of the integral manifolds are also presented. The application of the proposed impulsive control model is closely related to a most important problems in the mathematical biology—the problem of optimal control of epidemic models. The considered impulsive effects can be used by epidemiologists as a very effective therapy control strategy. In addition, since the integral manifolds approach is relevant in various contexts, our results can be applied in the qualitative investigations of many problems in the epidemiology of diverse interest.

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“…In addition, the so-called impulsive control technique has been successfully adapted to many applied problems. For some excellent results in impulsive systems, impulsive inclusions and impulsive control strategies, we refer to [23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Impulsive Fractional Differential Inclusions and Almost Periodic Waves

Stamov

Stamova

2021

Mathematics

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In the present paper, the concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo fractional derivative. New results on the existence and uniqueness are established by using the theory of operator semigroups, Hausdorff measure of noncompactness, fixed point theorems and fractional calculus techniques. Applications to a class of fractional-order impulsive gene regulatory network (GRN) models are proposed to illustrate the results.

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Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations

Cited by 14 publications

References 51 publications

High-Performance Tracking for Piezoelectric Actuators Using Super-Twisting Algorithm Based on Artificial Neural Networks

High-Performance Tracking for Piezoelectric Actuators Using Super-Twisting Algorithm Based on Artificial Neural Networks

Impulsive Reaction-Diffusion Delayed Models in Biology: Integral Manifolds Approach

Impulsive Fractional Differential Inclusions and Almost Periodic Waves

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