Modulational instability in a coupled nonlocal media with cubic, quintic and septimal nonlinearities

Tchepemen, Nathan; Balasubramanian, Sudharsan; Kanagaraj, Nithyanandan; Kengne, Emmanuel

doi:10.1007/s11071-023-08951-4

Cited by 4 publications

(3 citation statements)

References 54 publications

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“…The core idea is as follows: within the selected optimization region, the residual signal is utilized between the actual output of actuator agent j in MAS (1) and the fault tracking estimation output. Further, the ILC protocol (10) is leveraged to adjust the introduced virtual faults. This adjustment is performed in such a way that the virtual faults gradually approach the true faults of actuator agent j in the MAS along the iteration axis.…”

Section: Design Of Fault Estimation Tracker and Learning Control Prot...mentioning

confidence: 99%

“…The successful completion of complex tasks through cooperation in MASs is contingent upon the normal operation of each agent and the maintenance of regular communication connections between agents [7]. However, unlike the single intelligent system described by ordinary differential equations (ODEs) in [8][9][10], with an increase in the number of agents, the long-term operation of MASs becomes more susceptible to the influence of failures in practice [11]. Suppose that faults should be promptly diagnosed and addressed after occurrence, the distributed nature of MASs makes faults prone to propagating among their networks, leading to MAS paralysis and causing severe economic losses [12].…”

Section: Introductionmentioning

confidence: 99%

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Distributed Fault Diagnosis via Iterative Learning for Partial Differential Multi-Agent Systems with Actuators

Wang,

Zhou,

Wang

2024

Mathematics

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Component failures can lead to performance degradation or even failure in multi-agent systems, thus necessitating the development of fault diagnosis methods. Addressing the distributed fault diagnosis problem in a class of partial differential multi-agent systems with actuators, a fault estimator is designed under the introduction of virtual faults to the agents. A P-type iterative learning control protocol is formulated based on the residual signals, aiming to adjust the introduced virtual faults. Through rigorous mathematical analysis utilizing contraction mapping and the Bellman–Gronwall lemma, sufficient conditions for the convergence of this protocol are derived. The results indicate that the learning protocol ensures the tracking of virtual faults to actual faults, thereby facilitating fault diagnosis for the systems. Finally, the effectiveness of the learning protocol is validated through numerical simulation.

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Section: Design Of Fault Estimation Tracker and Learning Control Prot...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distributed Fault Diagnosis via Iterative Learning for Partial Differential Multi-Agent Systems with Actuators

Wang,

Zhou,

Wang

2024

Mathematics

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“…Let us admit that, these sought perturbed solutions ψ (x, t) and ϕ (x, t) have the following form [53,54]:…”

Section: Modulational Instabilitymentioning

confidence: 99%

Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights

Fendzi-Donfack,

Fotoula,

Jantschi

et al. 2024

Preprint

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This work aims to delve exact physical wave solutions of nonlinear diﬀerential-diﬀerence equations with beta-derivative leading the conduction of nerve impulse dynamics in coupled nerve ﬁbers. The technique performed here names the polynomial expansion method. By employing a new variable through a fractional complex transformation, we turn the electrical model equation to a second-order elliptic nonlinear ordinary diﬀerential equation with two free parameters including the semi-discrete approximation. We extract short pulse, kink, anti-kink, singular kink/anti-kink and kink-rogue solitary waves as solutions of the derived elliptic nonlinear ordinary diﬀerential equations. By carrying out these various solutions, we peruse the dynamical behavior of the current nerve ﬁbers model by investigating their linear stability. We also study the dynamics of the model by applying the ﬁxed points theory and derive the related Jacobian matrix. Throughout the convenient physiological parameters values and signs, we display some 3D modulational instability zones. Furthermore, we also exhibit 3D and 2D graphs presenting the shapes of new pursued solitary waves. The numerous solutions families obtained and plotted help us to show the fractional-order parameter eﬀects in addition of the nerve ﬁber diameter on the amplitude and speed of the nerve impulse propagating inside the coupled nerve ﬁbers. The good or bad coordination of the movement inside the human parts can be explain through the amplitude varying, speed modiﬁcation of the nerve impulse ﬂowing into the coupled nerve ﬁbers. Aiming to this, we make the evolved mathematical framework accessible and highlight potential medical and biological applications. In addition, we enhance the understanding of nerve conduction mechanisms in myelinated ﬁbers.

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Chirped dark soliton propagation in optical fiber under a self phase modulation and a self-steepening effect for higher order nonlinear Schrödinger equation

Muniyappan,

Parasuraman,

Seadawy

et al. 2024

Opt Quant Electron

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Modulational instability in a coupled nonlocal media with cubic, quintic and septimal nonlinearities

Cited by 4 publications

References 54 publications

Distributed Fault Diagnosis via Iterative Learning for Partial Differential Multi-Agent Systems with Actuators

Distributed Fault Diagnosis via Iterative Learning for Partial Differential Multi-Agent Systems with Actuators

Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights

Chirped dark soliton propagation in optical fiber under a self phase modulation and a self-steepening effect for higher order nonlinear Schrödinger equation

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