arXiv subjects

Marius E. Yamakou

Publications and source records attributed to Marius E. Yamakou.

At least 19 recordsLinked to original sources

arXiv2026

Heterogeneity-enhanced stochastic resonance improves liquid-state computing in delayed spiking neural networks

We investigate the joint effects of stochastic forcing and quenched structural heterogeneity on stochastic resonance (SR) and liquid-state computation in a small-world network of excitable FitzHugh--Nagumo neurons. Heterogeneity is introduced separately through coupling strengths and time delays drawn from Gaussian, bimodal, and shifted-exponential distributions. Weak periodic forcing resolves the stochastic-resonance landscape, whereas weak aperiodic driving probes noise-assisted signal encoding and Liquid State Machine (LSM) forecasting. Heterogeneity is not generically beneficial, but reorganizes the resonance landscape and computational performance in a distribution-dependent manner. Gaussian coupling disorder broadens the strong-response region, whereas bimodal disorder produces a more pronounced enhancement and shifts resonance toward weaker noise. Shifted-exponential coupling disorder behaves differently: increasing its scale broadens and shifts the coupling distribution toward less responsive regions. Time-delay heterogeneity can enhance or suppress SR depending on how the delay distribution samples the structured delay-response landscape. Under aperiodic forcing, stronger input--output coherence accompanies lower LSM prediction error, showing that SR can improve LSM performance and that suitable coupling heterogeneity can further enhance this computational benefit; Gaussian and bimodal coupling disorder shift the optimum toward weaker noise and reduce the noise-optimized root-mean-square prediction error, with the largest reduction obtained for the bimodal case. These results identify stochastic forcing and quenched heterogeneity as coupled control parameters and show that the computational enhancement of LSMs depends on disorder structure rather than magnitude alone.

nlin.AO↗

arXiv2026

Interaction order controls stochastic-resonance enhancement and redistribution in delayed multiplex neural networks

We investigate stochastic resonance in a hierarchy of delayed excitable systems, from a single FitzHugh--Nagumo neuron to single-layer and duplex networks with autaptic, pairwise, triadic higher-order, and interlayer interactions. The response to weak periodic forcing is characterized by the spectral amplitude at the driving frequency, restricting the stochastic-resonance analysis to deterministically subthreshold regimes. We show that the order and organization of interactions generate distinct resonance regimes. Among the autapse-free single-layer architectures, pairwise coupling produces the largest attainable response, whereas weak triadic coupling minimizes the noise amplitude required for resonance. Delayed autaptic feedback primarily shifts the optimal noise level and, within the configurations investigated, yields a genuine enhancement only when pairwise and triadic interactions coexist, revealing a non-additive coupling effect. In duplex networks, interlayer coupling acts predominantly as a response-equalization mechanism: it enhances the weaker layer, generally at the expense of the stronger one, with the redistribution controlled mainly by the uncoupled resonance-capacity gap. Increasing the interlayer delay generally suppresses this collective response. These results identify interaction order, resonance mismatch, and delay as key control parameters for noise-assisted signal processing in multilayer excitable systems.

nlin.AO↗

arXiv2026

Analysis of inverse stochastic resonance: Effects of neural excitability and timescale separation

We analyze inverse stochastic resonance (ISR) in a bistable FitzHugh--Nagumo neuron driven by additive noise in the voltage variable, focusing on how neural excitability and timescale separation regulate the noise-induced modulation of spiking activity. A codimension-two bifurcation analysis identifies a narrow bistable region in which a stable fixed point and a stable limit cycle coexist, separated by an unstable periodic orbit. Finite-time Monte Carlo simulations show that the occupation of the limit-cycle basin may appear to depend on the initial basin when rare transitions are not fully resolved. We prove that this dependence is not asymptotic: the stochastic system admits a unique invariant probability measure, so long-time firing statistics are independent of the initial basin of attraction. The parameter dependence of ISR is characterized by quasi-potential barriers computed with a geometric minimum action method for the degenerate noise. The difference between the limit-cycle and fixed-point quasi-potentials partitions the bistable wedge into two escape-dominated regimes. A reduced metastable two-state Markov approximation yields a weak-noise formula for the limit-cycle basin occupation probability, a sign criterion for genuine ISR, and a semiquantitative prediction of the ISR-minimizing noise amplitude. In the fitted regime with a negative effective exponent, a genuine ISR minimum occurs only when the limit-cycle quasi-potential exceeds that of the fixed point. These results provide an escape-balance mechanism linking intrinsic neuronal parameters to asymptotic noise-induced spike suppression.

nlin.AO↗

arXiv2026

A Lyapunov stability proof and a port-Hamiltonian physics-informed neural network for chaotic synchronization in memristive neurons

We study chaotic synchronization in a 5D Hindmarsh--Rose neuron model augmented with electromagnetic induction and a switchable memristive autapse. For two diffusively coupled identical neurons, we derive the transverse error dynamical system and analyze local synchronization via the linearized error system around the synchronization manifold. A quadratic Lyapunov function yields explicit sufficient conditions for (i) asymptotic stability when the memristive switching remains dissipative and (ii) practical stability with an explicit ultimate bound under non-dissipative switching. We complement this with a Hamiltonian-based viewpoint: a Helmholtz decomposition of the linearized error vector field provides a closed-form synchronization Hamiltonian and its rate identity. Numerical simulations corroborate convergence or ultimate boundedness of the synchronization errors and an overall decay of the synchronization Hamiltonian and its instantaneous rate toward zero after transients, and show consistent trends between Lyapunov- and Hamiltonian-based diagnostics across parameters. Finally, we propose the first port-Hamiltonian physics-informed neural network (pH-PINN) that learns this synchronization Hamiltonian and its rate from data while preserving conservative/dissipative structure, achieving close agreement with the analytical expressions.

nlin.AO↗

arXiv2026

Self-induced stochastic resonance: A physics-informed machine learning approach

Self-induced stochastic resonance (SISR) is the emergence of coherent oscillations in slow-fast excitable systems driven solely by noise, without external periodic forcing or proximity to a bifurcation. This work presents a physics-informed machine learning framework for modeling and predicting SISR in the stochastic FitzHugh-Nagumo neuron. We embed the governing stochastic differential equations and SISR-asymptotic timescale-matching constraints directly into a Physics-Informed Neural Network (PINN) based on a Noise-Augmented State Predictor architecture. The composite loss integrates data fidelity, dynamical residuals, and barrier-based physical constraints derived from Kramers' escape theory. The trained PINN accurately predicts the dependence of spike-train coherence on noise intensity, excitability, and timescale separation, matching results from direct stochastic simulations with substantial improvements in accuracy and generalization compared with purely data-driven methods, while requiring significantly less computation. The framework provides a data-efficient and interpretable surrogate model for simulating and analyzing noise-induced coherence in multiscale stochastic systems.

cs.LG↗

arXiv2025

Effect of diversity distribution symmetry on global oscillations of networks of excitable units

We investigate the role of the degree of symmetry of the diversity distribution in shaping the collective dynamics of networks of coupled excitable units modeled by FitzHugh-Nagumo equations. While previous studies have focused primarily on the ratio between the numbers of individually oscillatory and excitable units, we show that the symmetry of the diversity distribution plays a fundamental role in the emergence of global network oscillations. By exploring various symmetric and asymmetric distributions and simulating network dynamics across various topologies, we demonstrate that symmetric distributions promote resonant collective oscillations even in the absence of oscillatory units. We propose two quantitative metrics, the normalized center of mass and the symmetry balance score, to assess the degree of symmetry and predict the presence or absence of global oscillations. By studying a minimal two-unit system and its effective pseudo-potential, we show that symmetry enables the formation of a landscape characterized by a cyclic valley supporting limit cycles, whereas asymmetry collapses the system into a single non-oscillatory equilibrium. These results provide a general mechanism by which network symmetry drives emergent synchronization in heterogeneous excitable systems.

nlin.AO↗

arXiv2025

Dynamical equivalence between resonant translocation of a polymer chain and diversity-induced resonance

Networks of heterogeneous oscillators are often seen to display collective synchronized oscillations, even when single elements of the network do not oscillate in isolation. It has been found that it is the diversity of the individual elements that drives the phenomenon, possibly leading to the appearance of a resonance in the response. Here we study the way in which heterogeneity acts in producing an oscillatory regime in a network and show that the resonance response is based on the same physics underlying the resonant translocation regime observed in models of polymer diffusion on a substrate potential. Such a mechanical analog provides an alternative viewpoint that is useful to interpret and understand the nature of collective oscillations in heterogeneous networks.

physics.bio-ph↗

arXiv2024

Inverse stochastic resonance in adaptive small-world neural networks

Inverse stochastic resonance (ISR) is a phenomenon where noise reduces rather than increases the firing rate of a neuron, sometimes leading to complete quiescence. ISR was first experimentally verified with cerebellar Purkinje neurons. These experiments showed that ISR enables optimal information transfer between the input and output spike train of neurons. Subsequent studies demonstrated the efficiency of information processing and transfer in neural networks with small-world topology. We conducted a numerical investigation into the impact of adaptivity on ISR in a small-world network of noisy FitzHugh-Nagumo (FHN) neurons, operating in a bistable regime with a stable fixed point and a limit cycle -- a prerequisite for ISR. Our results show that the degree of ISR is highly dependent on the FHN model's timescale separation parameter $ε$. The network structure undergoes dynamic adaptation via mechanisms of either spike-time-dependent plasticity (STDP) with potentiation-/depression-domination parameter $P$, or homeostatic structural plasticity (HSP) with rewiring frequency $F$. We demonstrate that both STDP and HSP amplify ISR when $ε$ lies within the bistability region of FHN neurons. Specifically, at larger values of $ε$ within the bistability regime, higher rewiring frequencies $F$ enhance ISR at intermediate (weak) synaptic noise intensities, while values of $P$ consistent with depression-domination (potentiation-domination) enhance (deteriorate) ISR. Moreover, although STDP and HSP parameters may jointly enhance ISR, $P$ has a greater impact on ISR compared to $F$. Our findings inform future ISR enhancement strategies in noisy artificial neural circuits, aiming to optimize information transfer between input and output spike trains in neuromorphic systems, and prompt venues for experiments in neural networks.

nlin.AO↗

arXiv2024

Reduced-order adaptive synchronization in a chaotic neural network with parameter mismatch: A dynamical system vs. machine learning approach

In this paper, we address the reduced-order synchronization problem between two chaotic memristive Hindmarsh-Rose (HR) neurons of different orders using two distinct methods. The first method employs the Lyapunov active control technique. Through this technique, we develop appropriate control functions to synchronize a 4D chaotic HR neuron (response system) with the canonical projection of a 5D chaotic HR neuron (drive system). Numerical simulations are provided to demonstrate the effectiveness of this approach. The second method is data-driven and leverages a machine learning-based control technique. Our technique utilizes an ad hoc combination of reservoir computing (RC) algorithms, incorporating reservoir observer (RO), online control (OC), and online predictive control (OPC) algorithms. We anticipate our effective heuristic RC adaptive control algorithm to guide the development of more formally structured and systematic, data-driven RC control approaches to chaotic synchronization problems, and to inspire more data-driven neuromorphic methods for controlling and achieving synchronization in chaotic neural networks in vivo.

nlin.AO↗

arXiv2024

Dynamics of neural fields with exponential temporal kernel

We consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of neurons, which Green's function does not. Through a dynamic bifurcation analysis, we give explicit bifurcation conditions. Hopf bifurcations lead to temporally non-constant, but spatially constant solutions, but Turing-Hopf bifurcations generate spatially and temporally non-constant solutions, in particular, traveling waves. Bifurcation parameters are the coefficient of the exponential temporal kernel, the transmission speed of neural signals, the time delay rate of synapses, and the ratio of excitatory to inhibitory synaptic weights.

math.DS↗

arXiv2023

Quantifying and maximizing the information flux in recurrent neural networks

Free-running Recurrent Neural Networks (RNNs), especially probabilistic models, generate an ongoing information flux that can be quantified with the mutual information $I\left[\vec{x}(t),\vec{x}(t\!+\!1)\right]$ between subsequent system states $\vec{x}$. Although, former studies have shown that $I$ depends on the statistics of the network's connection weights, it is unclear (1) how to maximize $I$ systematically and (2) how to quantify the flux in large systems where computing the mutual information becomes intractable. Here, we address these questions using Boltzmann machines as model systems. We find that in networks with moderately strong connections, the mutual information $I$ is approximately a monotonic transformation of the root-mean-square averaged Pearson correlations between neuron-pairs, a quantity that can be efficiently computed even in large systems. Furthermore, evolutionary maximization of $I\left[\vec{x}(t),\vec{x}(t\!+\!1)\right]$ reveals a general design principle for the weight matrices enabling the systematic construction of systems with a high spontaneous information flux. Finally, we simultaneously maximize information flux and the mean period length of cyclic attractors in the state space of these dynamical networks. Our results are potentially useful for the construction of RNNs that serve as short-time memories or pattern generators.

q-bio.NC↗

arXiv2023

Synchronization in STDP-driven memristive neural networks with time-varying topology

Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons driven by spike-timing-dependent plasticity (STDP) and temporal networks subject to homeostatic structural plasticity (HSP) rules remain unclear. Here, we bridge this gap by determining the configurations required to achieve high and stable degrees of complete synchronization (CS) and phase synchronization (PS) in time-varying small-world and random neural networks driven by STDP and HSP. In particular, we found that decreasing $P$ (which enhances the strengthening effect of STDP on the average synaptic weight) and increasing $F$ (which speeds up the swapping rate of synapses between neurons) always lead to higher and more stable degrees of CS and PS in small-world and random networks, provided that the network parameters such as the synaptic time delay $τ_c$, the average degree $\langle k \rangle$, and the rewiring probability $β$ have some appropriate values. When $τ_c$, $\langle k \rangle$, and $β$ are not fixed at these appropriate values, the degree and stability of CS and PS may increase or decrease when $F$ increases, depending on the network topology. It is also found that the time delay $τ_c$ can induce intermittent CS and PS whose occurrence is independent $F$. Our results could have applications in designing neuromorphic circuits for optimal information processing and transmission via synchronization phenomena.

q-bio.NC↗

arXiv2023

Self-induced-stochastic-resonance breathing chimeras

The study in [Phys. Rev. Lett. 117, 014102 (2016)] discovered a novel type of chimera state known as coherence-resonance chimera (CRC), which combines the effects of coherence resonance (CR) and the spatial property of classical chimeras. In this Letter, we present yet another novel form of chimera, which we refer to as self-induced-stochastic-resonance breathing chimera (SISR-BC), which differs fundamentally from the CRC in that it combines the mechanism and effects of self-induced stochastic resonance (SISR, previously shown in [Phys. Rev. E 72, 031105 (2005)] to be intrinsically different from CR), the symmetry breaking in the rotational coupling between the slow and fast subsystems of the coupled oscillators, and the property of breathing chimera -- a form of chimera state characterized by non-stationary periodic dynamics of coherent-incoherent patterns with a periodically oscillating global order parameter. Unlike other types of chimeras, including CRC, SISR-BC demonstrates remarkable resilience to a relatively wide range of stochastic perturbations and persists even when the purely excitable system is significantly distant from the Hopf bifurcation threshold -- thanks to the mechanism of SISR -- and globally attract random distributions of initial conditions. Considering its potential impact on information processing in neuronal networks, SISR-BC could have special significance and applications.

nlin.AO↗

arXiv2023

Combined effects of STDP and homeostatic structural plasticity on coherence resonance

Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus, this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter $P$, which controls STDP, on the characteristic rewiring frequency parameter $F$, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors: (i) Decreasing $P$ (which enhances the weakening effect of STDP on synaptic weights) and decreasing $F$ (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter $τ_c$ has some appropriate values. (ii) Increasing the synaptic time delay $τ_c$ induces multiple CR (MCR) -- the occurrence of multiple peaks in the degree of coherence as $τ_c$ changes -- in small-world and random networks, with MCR becoming more pronounced at smaller values of $P$ and $F$. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.

q-bio.NC↗

arXiv2023

Coherence resonance and stochastic synchronization in a small-world neural network: An interplay in the presence of spike-timing-dependent plasticity

Coherence resonance (CR), stochastic synchronization (SS), and spike-timing-dependent plasticity (STDP) are ubiquitous dynamical processes in biological neural networks. Whether there exists an optimal network and STDP configuration at which CR and SS are both pronounced is a fundamental question of interest that is still elusive. We expect such a configuration to enable the brain to make synergistic and optimal use of these phenomena to process information efficiently. This paper considers a small-world network of excitable Hodgkin-Huxley neurons driven by channel noise and STDP with an asymmetric Hebbian time window. Numerical results indicate specific network topology and STDP parameter intervals in which CR and SS can be simultaneously enhanced. Our results imply that an optimally tuned inherent background noise, STDP rule, and network topology can play a constructive role in enhancing both the time precision of firing and the synchronization in neural systems.

q-bio.NC↗

arXiv2022

Diversity-induced decoherence

We analyze the effect of small-amplitude noise and heterogeneity in a network of coupled excitable oscillators with strong time scale separation. Using mean-field analysis, we uncover the mechanism of a new nontrivial effect -- diversity-induced decoherence (DIDC) -- in which heterogeneity modulates the mechanism of self-induced stochastic resonance to inhibit the coherence of oscillations. We argue that DIDC may offer one possible mechanism via which, in excitable neural systems, generic heterogeneity and background noise can synergistically prevent unwanted resonances that may be related to hyperkinetic movement disorders.

nlin.AO↗

arXiv2021

Control of noise-induced coherent oscillations in three-neuron motifs

The phenomenon of self-induced stochastic resonance (SISR) requires a nontrivial scaling limit between the deterministic and the stochastic timescales of an excitable system, leading to the emergence of coherent oscillations which are absent without noise. In this paper, we numerically investigate SISR and its control in single neurons and three-neuron motifs made up of the Morris-Lecar model. In single neurons, we compare the effects of electrical and chemical autapses on the degree of coherence of the oscillations due to SISR. In the motifs, we compare the effects of altering the synaptic time-delayed couplings and the topologies on the degree of SISR. Finally, we provide two enhancement strategies for a particularly poor degree of SISR in motifs with chemical synapses: (i) we show that a poor SISR can be significantly enhanced by attaching an electrical or an excitatory chemical autapse on one of the neurons, and (ii) we show that by multiplexing the motif with a poor SISR to another motif (with a high SISR in isolation), the degree of SISR in the former motif can be significantly enhanced. We show that the efficiency of these enhancement strategies depends on the topology of the motifs and the nature of synaptic time-delayed couplings mediating the multiplexing connections.

nlin.AO↗

arXiv2021

Levy noise-induced self-induced stochastic resonance in a memristive neuron

Self-induced stochastic resonance (SISR) is a subtle resonance mechanism requiring a nontrivial scaling limit between the stochastic and the deterministic timescales of an excitable system, leading to the emergence of a limit cycle behavior which is absent without noise. All previous studies on SISR in neural systems have only considered the idealized Gaussian white noise. Moreover, these studies have ignored one electrophysiological aspect of the nerve cell: its memristive properties. In this paper, first, we show that in the excitable regime, the asymptotic matching of the Levy timescale (that follows a power law, unlike Gaussian noise that follows Kramers law) and the deterministic timescale (controlled by the singular parameter) can also induce a strong SISR. In addition, it is shown that the degree of SISR induced by Levy noise is not always higher than that of Gaussian noise. Second, we show that, for both types of noises, the two memristive properties of the neuron have opposite effects on the degree of SISR: the stronger the feedback gain parameter that controls the modulation of the membrane potential with the magnetic flux and the weaker the feedback gain parameter that controls the saturation of the magnetic flux, the higher the degree of SISR. Finally, we show that, for both types of noises, the degree of SISR in the memristive neuron is always higher than in the non-memristive neuron. Our results could find applications in designing neuromorphic circuits operating in noisy regimes.

nlin.AO↗