Search Results (12)

Neuromorphic circuits emulate the brain’s massively parallel, energy-efficient, and robust information processing by reproducing the behavior of neurons and synapses in dense networks. Memristive technologies have emerged as key enablers of such systems, offering compact and low-power implementations. In particular, locally active memristors (LAMs), with their ability to amplify small perturbations within a locally active domain to generate action potential-like responses, provide powerful building blocks for neuromorphic circuits and offer new perspectives on the mechanisms underlying neuronal firing dynamics. This paper introduces a novel second-order locally active memristor (LAM) governed by two coupled state variables, enabling richer nonlinear dynamics compared to conventional first-order devices. Even when the capacitances controlling the states are equal, the device retains two independent memory states, which broaden the design space for hysteresis tuning and allow flexible modulation of the current–voltage response. The second-order LAM is then integrated into a FitzHugh–Nagumo neuron circuit. The proposed circuit exhibits oscillatory firing behavior under specific parameter regimes and is further investigated under both DC and AC external stimulation. A comprehensive analysis of its equilibrium points is provided, followed by bifurcation diagrams and Lyapunov exponent spectra for key system parameters, revealing distinct regions of periodic, chaotic, and quasi-periodic dynamics. Representative time-domain patterns corresponding to these regimes are also presented, highlighting the circuit’s ability to reproduce a rich variety of neuronal firing behaviors. Finally, two unknown system parameters are estimated using the Aquila Optimization algorithm, with a cost function based on the system’s return map. Simulation results confirm the algorithm’s efficiency in parameter estimation. Full article

Recent research and instances have demonstrated that most real-world systems can be effectively schematized by multiplex networks. Moreover, the interactions within systems often emerge among triadic or tetradic interactions, or even interactions with more element combinations, in addition to pairwise interactions. Hypergraph coupling structures are particularly well-suited for capturing such arbitrary higher-order interactions among nodes, thereby playing a key role in accurately depicting system dynamics. Meanwhile, the functionality of numerous complex systems depends on synchronization mechanisms. Therefore, this paper focuses on investigating the synchronous stability of a multiplex hypergraph. Specifically, we examine a three-layer network where intralayer interactions are represented by hyperedges, while the interlayer interactions are modeled through pairwise couplings. By generalizing the master stability function approach to the hypergraph structure, the synchronization phenomenon of such multiplex hypergraphs is analyzed. To verify our theoretical conclusions, we apply the proposed framework to networks of FitzHugh–Nagumo neurons and Rikitake two-disk dynamos. Simulation results unveil that the presence of higher-order interactions enhances the synchronous ability within the multiplex framework. Full article

This paper consists of various kinds of wave solitons to the mathematical model known as the truncated M-fractional FitzHugh–Nagumo model. This model explains the transmission of the electromechanical pulses in nerves. Through the application of the modified extended tanh function technique and the modified $(G^{\prime }/G^2)$-expansion technique, we are able to achieve the series of exact solitons. The results differ from the current solutions because of the fractional derivative. These solutions could be helpful in the telecommunication and bioscience domains. Contour plots, in two and three dimensions, are used to describe the results. Stability analysis is used to check the stability of the obtained solutions. Moreover, the stationary solutions of the focusing equation are studied through modulation instability. Future research on the focused model in question will benefit from the findings. The techniques used are simple and effective. Full article

Understanding the intricate and dynamic nature of brain disorders, such as epilepsy, Parkinson’s disease, and schizophrenia, presents a formidable challenge due to their inherent chaotic properties, which defy conventional analytical approaches. In response to this challenge, our research introduces a groundbreaking methodology aimed at simulating the chaotic behavior characteristic of these neurological conditions using advanced electrical circuit models. By conceptualizing the interactions among neurons and synapses as electrical components within our model, we endeavor to unravel the complex underlying mechanisms driving these disorders. Leveraging insights from chaos theory and drawing upon the rich toolkit of electrical engineering, our simulation framework offers a novel perspective on the ways in which disruptions within neural circuits manifest as pathological states, shedding light on the intricate dynamics of brain diseases. Through rigorous numerical simulations and thorough analysis, we illustrate the efficacy of our approach in deciphering the chaotic dynamics inherent in these disorders, thus laying the foundation for the development of innovative therapeutic interventions. Furthermore, our research underscores the paramount importance of fostering interdisciplinary collaboration between the fields of neuroscience and electrical engineering; as such, synergistic partnerships hold the key to unlocking new frontiers in understanding and effectively treating complex neurological disorders, thus paving the way for improved patient outcomes and enhanced quality of life. Full article

Transcranial electrical stimulation (tES) is increasingly recognized for its potential to modulate cerebral blood flow (CBF) and evoke cerebrovascular reactivity (CVR), which are crucial in conditions like mild cognitive impairment (MCI) and dementia. This study explores the impact of tES on the neurovascular unit (NVU), employing a physiological modeling approach to simulate the vascular response to electric fields generated by tES. Utilizing the FitzHugh–Nagumo model for neuroelectrical activity, we demonstrate how tES can initiate vascular responses such as vasoconstriction followed by delayed vasodilation in cerebral arterioles, potentially modulated by a combination of local metabolic demands and autonomic regulation (pivotal locus coeruleus). Here, four distinct pathways within the NVU were modeled to reflect the complex interplay between synaptic activity, astrocytic influences, perivascular potassium dynamics, and smooth muscle cell responses. Modal analysis revealed characteristic dynamics of these pathways, suggesting that oscillatory tES may finely tune the vascular tone by modulating the stiffness and elasticity of blood vessel walls, possibly by also impacting endothelial glycocalyx function. The findings underscore the therapeutic potential vis-à-vis blood-brain barrier safety of tES in modulating neurovascular coupling and cognitive function needing the precise modulation of NVU dynamics. This technology review supports the human-in-the-loop integration of tES leveraging digital health technologies for the personalized management of cerebral blood flow, offering new avenues for treating vascular cognitive disorders. Future studies should aim to optimize tES parameters using computational modeling and validate these models in clinical settings, enhancing the understanding of tES in neurovascular health. Full article

In this paper, a numerical approach employing radial basis functions has been applied to solve time-fractional FitzHugh–Nagumo equation. Spatial approximation is achieved by combining radial basis functions with the collocation method, while temporal discretization is accomplished using a finite difference scheme. To evaluate the effectiveness of this method, we first conduct an eigenvalue stability analysis and then validate the results with numerical examples, varying the shape parameter c of the radial basis functions. Notably, this method offers the advantage of being mesh-free, which reduces computational overhead and eliminates the need for complex mesh generation processes. To assess the method’s performance, we subject it to examples. The simulated results demonstrate a high level of agreement with exact solutions and previous research. The accuracy and efficiency of this method are evaluated using discrete error norms, including ${\mathrm{L}}_2$, ${\mathrm{L}}_{\infty }$, and ${\mathrm{L}}_{rms}$. Full article

The aim of this work is to describe the dynamics of a discrete fractional-order reaction–diffusion FitzHugh–Nagumo model. We established acceptable requirements for the local asymptotic stability of the system’s unique equilibrium. Moreover, we employed a Lyapunov functional to show that the constant equilibrium solution is globally asymptotically stable. Furthermore, numerical simulations are shown to clarify and exemplify the theoretical results. Full article

In this paper, the transport phenomena of synaptic electric impulses are considered. The FitzHugh–Nagumo and FitzHugh–Rinzel models appear mathematically appropriate for evaluating these scientific issues. Moreover, applications of such models arise in several biophysical phenomena in different fields such as, for instance, biology, medicine and electronics, where, by means of nanoscale memristor networks, scientists seek to reproduce the behavior of biological synapses. The present article deals with the properties of the solutions of the FitzHugh–Rinzel system in an attempt to achieve, by means of a suitable “energy function”, conditions ensuring the boundedness and existence of absorbing sets in the phase space. The results obtained depend on several parameters characterizing the system, and, as an example, a concrete case is considered. Full article

As efficient separation of variables plays a central role in model reduction for nonlinear and nonaffine parameterized systems, we propose a stochastic discrete empirical interpolation method (SDEIM) for this purpose. In our SDEIM, candidate basis functions are generated through a random sampling procedure, and the dimension of the approximation space is systematically determined by a probability threshold. This random sampling procedure avoids large candidate sample sets for high-dimensional parameters, and the probability based stopping criterion can efficiently control the dimension of the approximation space. Numerical experiments are conducted to demonstrate the computational efficiency of SDEIM, which include separation of variables for general nonlinear functions, e.g., exponential functions of the Karhu nen–Loève (KL) expansion, and constructing reduced order models for FitzHugh–Nagumo equations, where symmetry among limit cycles is well captured by SDEIM. Full article

The neurovascular unit (NVU) concept denotes cells and their communication mechanisms that autoregulate blood supply in the brain parenchyma. Over the past two decades, it has become clear that besides its primary function, NVU is involved in many important processes associated with maintaining brain health and that altering the proportion of the extracellular space plays a vital role in this. While biologists have studied the process of cells swelling or shrinking, the consequences of the NVU’s operation are not well understood. In addition to direct quantitative modeling of cellular processes in the NVU, there is room for developing a minimalistic mathematical description, similar to how computational neuroscience operates with very simple models of neurons, which, however, capture the main features of dynamics. In this work, we have developed a minimalistic model of cell volumes regulation in the NVU. We based our model on the FitzHugh–Nagumo model with noise excitation and supplemented it with a variable extracellular space volume. We show that such a model acquires new dynamic properties in comparison with the traditional neuron model. To validate our approach, we adjusted the parameters of the minimalistic model so that its behavior fits the dynamics computed using the high-dimensional quantitative and biophysically relevant model. The results show that our model correctly describes the change in cell volume and intercellular space in the NVU. Full article

A theoretical and computational study on the estimation of the parameters of a single Fitzhugh–Nagumo model is presented. The difference of this work from a conventional system identification is that the measured data only consist of discrete and noisy neural spiking (spike times) data, which contain no amplitude information. The goal can be achieved by applying a maximum likelihood estimation approach where the likelihood function is derived from point process statistics. The firing rate of the neuron was assumed as a nonlinear map (logistic sigmoid) relating it to the membrane potential variable. The stimulus data were generated by a phased cosine Fourier series having fixed amplitude and frequency but a randomly shot phase (shot at each repeated trial). Various values of amplitude, stimulus component size, and sample size were applied to examine the effect of stimulus to the identification process. Results are presented in tabular and graphical forms, which also include statistical analysis (mean and standard deviation of the estimates). We also tested our model using realistic data from a previous research (H1 neurons of blowflies) and found that the estimates have a tendency to converge. Full article

We develop a completely data-driven approach to reconstructing coupled neuronal networks that contain a small subset of chaotic neurons. Such chaotic elements can be the result of parameter shift in their individual dynamical systems and may lead to abnormal functions of the network. To accurately identify the chaotic neurons may thus be necessary and important, for example, applying appropriate controls to bring the network to a normal state. However, due to couplings among the nodes, the measured time series, even from non-chaotic neurons, would appear random, rendering inapplicable traditional nonlinear time-series analysis, such as the delay-coordinate embedding method, which yields information about the global dynamics of the entire network. Our method is based on compressive sensing. In particular, we demonstrate that identifying chaotic elements can be formulated as a general problem of reconstructing the nodal dynamical systems, network connections and all coupling functions, as well as their weights. The working and efficiency of the method are illustrated by using networks of non-identical FitzHugh–Nagumo neurons with randomly-distributed coupling weights. Full article