Stability analysis of fractional order memristor synapse-coupled hopfield neural network with ring structure

Eftekhari, Leila; Amirian, Mohammad M.

doi:10.1007/s11571-022-09844-9

Cited by 20 publications

(8 citation statements)

References 46 publications

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“…A variety of approximate analytical methods were presented [30][31][32][33][34]. Further relevant works were carried out in [26,[35][36][37][38].…”

Section: Discussionmentioning

confidence: 99%

“…By inserting equation (38) in equation ( 9), the real part system and complex part system are respectively given by, 29), and (30), is called Six-dimension extended complex Finance Model (6DECFM)…”

Section: Six-dimension Complex Finance Model (6d-cfm)mentioning

confidence: 99%

“…with P = (0, 0, 0) is an equilibrium point of equation (9) (or equation(38)). In equation(9), for the extended center manifold (ECM) it is required that, det A 0, ¹ so a .To construct ECM: Γ, we proceed by setting a ,…”

mentioning

confidence: 99%

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Analytic solutions of alpha-beta -time- derivatives complex finance chaotic dynamical system: synchronization and extended center manifold. An explicit approach

Abdel-Gawad,

El Mahdy

2024

Phys. Scr.

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The present study focuses on a real finance nonlinear dynamic system (FNLDS), which has been shown to exhibit chaotic behavior. The solutions for such nonlinear dynamical systems (NLDSs) have typically been derived using numerical techniques. The objective of this study aims to; firstly, derive approximate analytical solutions for the complex FNLDS (CFNLDS) by constructing the Picard iterative scheme. The convergence of this scheme is proven, and the error analysis shows good tolerance, indicating the efficiency of the technique. Second a novel criterion for synchronizing the real and imaginary parts of the system is presented, based on a necessary condition. Thirdly, a new method for constructing the extended center manifold is introduced. The 3D portrait reveals a feedback scroll pattern, while the 2D portrait, representing the mutual components, shows multiple pools. The synchronization of the real and imaginary parts of the system is demonstrated graphically. The FNLDS is tested for sensitivity dependence against infinitesimal variations in the initial conditions, and it is found that the system components are moderately sensitive. Furthermore, the Hamiltonian and the extended center manifold establish a two-fold structure. It is observed that the effect of the α−β derivative leads to delay the behavior of the solutions.

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“…A variety of approximate analytical methods were presented [30][31][32][33][34]. Further relevant works were carried out in [26,[35][36][37][38].…”

Section: Discussionmentioning

confidence: 99%

Section: Six-dimension Complex Finance Model (6d-cfm)mentioning

confidence: 99%

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Analytic solutions of alpha-beta -time- derivatives complex finance chaotic dynamical system: synchronization and extended center manifold. An explicit approach

Abdel-Gawad,

El Mahdy

2024

Phys. Scr.

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“…The resistance of memristors [1,2] can be adjusted, and their resistance state can be retained even after power-off. The feature is highly like neuronal synapses [3,4]. As two-terminal devices, they bear structural resemblance to biological synapses and offer the advantages of low power consumption and high integration density compared to traditional electronic synapses, garnering attention from scholars worldwide.…”

Section: Introductionmentioning

confidence: 99%

Dynamic symmetrization in a memristive HR neuron

Huang,

Li,

et al. 2024

Electronics Letters

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The significance of neuronal discharge symmetry lies in its reflection of the stability and orderliness within the neuron's activity. This symmetry is correlated with various issues, including the biophysical properties within neurons, network structures, and synaptic transmission. Memristors are highly analogous to neuronal synapses due to their unique memory properties, allowing them to emulate biological neural synapses. In this work, a memristor is employed into the Hindmarsh‐Rose (HR) neuron as a synapse for the construction of a memristive HR neuron. Accompanied with the introducing of the absolute value and signum function, the derived neurons exhibit complex coexisting symmetric firing patterns. The phenomenon of symmetric firing can effectively simulate the depolarization and hyperpolarization processes of neurons, providing a new approach to study the diversity of the brain.

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“…Our model combines the fixed composition of the Monod model with a more complex growth function that approximates a memory of the past history of extracellular conditions, allowing the growth rate to change as resources are depleted and mimicking the predictions of the Droop model. We use a fractional calculus extension of ordinary differential equations to include the past, in acclimation time scale, in addition to the current state of the system into the dynamical equations (Matlob and Jamali, 2019;Eftekhari and Amirian, 2022). Here we provide a theoretical justification for the model formulation, explore the mathematical, physical and biological interpretation of its parameters and equilibrium conditions, suggest a way to measure the cell memory empirically, and demonstrate its performance compared to Monod and Droop models with both simulations and experimental data from the laboratory.…”

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confidence: 99%

Extending the Monod model of microbal growth with memory

2022

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Monod’s model describes the growth of microorganisms using a hyperbolic function of extracellular resource concentration. Under fluctuating or limited resource concentrations this model performs poorly against experimental data, motivating the more complex Droop model with a time-varying internal storage pool. We extend the Monod model to incorporate memory of past conditions, adding a single parameter motivated by a fractional calculus analysis. We show how to interpret the memory element in a biological context and describe its connection to a resource storage pool. Under nitrogen starvation at non-equilibrium conditions, we validate the model with simulations and empirical data obtained from lab cultures of diatoms (T. pseudonana and T. weissflogii) and prasinophytes (Micromonas sp. and O. tauri), globally influential phytoplankton taxa. Using statistical analysis, we show that our Monod-memory model estimates the growth rate, cell density and resource concentration as well as the Droop model, while requiring one less state variable. Our simple model may improve descriptions of phytoplankton dynamics in complex earth system models at a lower computational cost than is presently achievable.

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Stability analysis of fractional order memristor synapse-coupled hopfield neural network with ring structure

Cited by 20 publications

References 46 publications

Analytic solutions of alpha-beta -time- derivatives complex finance chaotic dynamical system: synchronization and extended center manifold. An explicit approach

Analytic solutions of alpha-beta -time- derivatives complex finance chaotic dynamical system: synchronization and extended center manifold. An explicit approach

Dynamic symmetrization in a memristive HR neuron

Extending the Monod model of microbal growth with memory

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