Nonidentical Neurons Research Articles

Synchronization of two non-identical Chialvo neurons

We investigate the synchronization between two neurons using the stochastic version of the map-based Chialvo model. To simulate non-identical neurons, a mismatch is introduced in one of the main parameters of the model. Subsequently, the synchronization of the neurons is studied as a function of this mismatch, the noise introduced in the stochastic model, and the coupling strength between the neurons. We propose the simplest neural network for study, as its analysis is more straightforward and does not compromise generality. Within this network, two non-identical neurons are electrically coupled. In order to understand whether specific behaviors affect the global behavior of the system, we consider different cases related to the behavior of the neurons (chaotic or periodic). Furthermore, we study how variations in model parameters affect the firing frequency in each case. Additionally, we consider that the two neurons have both excitatory and inhibitory couplings. Consequently, we identify critical values of noise and mismatch for achieving satisfactory synchronization between the neurons in each case. Finally, we propose that the results have general applicability across various neuron models.

Creation of heterogeneity or defects in a memristive neural network under energy flow

The field energy in neuron can be changed under shape deformation because of external energy injection into the media. The electromagnetic field superposition enables energy pumping when neurons in the same region are stimulated, and synaptic connection can be created adaptively for keeping local energy balance. All neurons will keep energy balance with the adjacent neurons in the network by continuous energy propagation and exchange, and identical neurons will develop a homogeneous state while non-identical neurons will support formation of gradient spatial patterns. In this paper, the simple Fitzhugh–Nagumo (FHN) neural circuit is improved by incorporating a thermistor and a phototube in different branch circuits synchronously, and this neuron becomes sensitive to light and temperature. The Hamilton energy for this functional neuron is obtained to discern the dependence of firing modes on the energy level. These functional neurons are clustered to build a regular network via memristive synapses, and the creation and growth of memristive synapse can be controlled by energy diversity between adjacent neurons. It is found that heterogeneity in the network can be formed when more energy is accumulated locally, while the occurrence of local defects results from energy release and lower energy in a local area. As a result, shape deformation occurs and some parameters for the neurons covered with heterogeneity or defects show certain changes with time. The collective behaviors of the network are investigated by calculating the membrane potentials for neurons, Hamilton energy, coupling intensity and synchronization factor. The results indicate that energy diversity between neurons controls the occurrence of heterogeneity and defects in the network and local energy injection can control the firing patterns of network because the wave propagation can be regulated by the heterogeneity and defects.

Novel method to detect Hopf bifurcation in a delayed fractional-order network model with bidirectional ring structure

In this paper, we formulate and study a fractional-order network model with four neurons, bidirectional ring structure and self-delay feedback. For the scenario of non-identical neurons, we develop a new algebraic technique to deal with the characteristic equation with [Formula: see text] ([Formula: see text] is the self-feedback delay) term and thus establish the easy-to-check criteria to determine the Hopf bifurcation point of self-feedback delay by fixing communication delay in its stable interval. For the scenario of identical neurons, we apply the crossing curves method to the fractional functional equations and thus procure the Hopf bifurcation curve. The obtained results accommodate the fact that the model cannot preserve its stability behavior when the self-feedback delay crosses the Hopf bifurcation point in the positive direction. Finally, we deliberate on the correctness of our methodology through two demonstration examples.

Creation of synaptic connection to memristive neurons under noise

Continuous pumping of intracellular and extracellular ions can induce distinct electromagnetic induction accompanied by the channel current. The external electric stimuli and electromagnetic radiation can change the inner field energy in biological neurons, and the firing mode is regulated to discern the energy information in the neurons. The involvement of memristive channel can estimate the effect of electromagnetic field of an isolated neuron, which is sensitive to discern and capture external field energy under electromagnetic field. When two or more neurons with energy diversity are clustered, the synaptic connection is awaken and created with increasing coupling intensity until reaching complete synchronization. In this paper, the memristive Hodgkin–Huxley neuron model is used to discuss the synchronization stability when two neurons with energy diversity are clustered, two identical neurons can be coupled adaptive for reaching complete synchronization and perfect energy balance. In case of electromagnetic radiation, synchronization stability is controlled with increasing the coupling intensity adaptively by imposing noisy disturbance on the magnetic flux variable, which is used to describe the effect of magnetic field. For non-identical neurons, the creation and enhancement of synaptic connection are also realized because of energy diversity between two neurons.

Chimera states in a thermosensitive FitzHugh-Nagumo neuronal network

Temperature can affect the action potential of a neuron such that the firing pattern is changed under its variation. To incorporate the effects of the temperature, recently, a thermosensitive neuron was proposed in which a thermistor was added to a simple FitzHugh-Nagumo neuron model. Here, thermosensitive neurons are studied to realize the consequence of the thermistor on the neurons’ collective behavior. For specific coupling strengths, the chimera state is developed. The parameter region of the occurrence of the chimera state is obtained by computing the strength of incoherence and shows that the occurrence of the chimera is highly dependent on the coefficient of temperature change in the thermistor. Since, in reality, the neurons are not identical and also the thermistors are not precisely the same, the network is further considered with non-identical neurons. For this purpose, the coefficient of temperature changes in thermistors is not fixed and selected randomly from a normal distribution. The results show that for distributions with a small standard deviation, the behavior of the network changes slightly. While with increasing the standard deviation, the synchronization is achieved for higher coupling strengths, and the region of chimera is extended. Furthermore, although in the asynchronous network the neurons have different attractors, by the appearance of coherent groups and creation of the chimera, the attractors become identical.

Assortativity-induced explosive synchronization in a complex neuronal network.

In this study, we consider a scale-free network of nonidentical Chialvo neurons, coupled through electrical synapses. For sufficiently strong coupling, the system undergoes a transition from completely out of phase synchronized to phase synchronized state. The principal focus of this study is to investigate the effect of the degree of assortativity over the synchronization transition process. It is observed that, depending on assortativity, bistability between two asymptotically stable states allows one to develop a hysteresis loop which transforms the phase transition from second order to first order. An expansion in the area of hysteresis loop is noticeable with increasing degree-degree correlation in the network. Our study also reveals that effective frequencies of nodes simultaneously go through a continuous or sudden transition to the synchronized state with the corresponding phases. Further, we examine the robustness of the results under the effect of network size and average degree, as well as diverse frequency setup. Finally, we investigate the dynamical mechanism in the process of generating explosive synchronization. We observe a significant impact of lower degree nodes behind such phenomena: in a positive assortative network the low degree nodes delay the synchronization transition.

Dynamical robustness and firing modes in multilayer memristive neural networks of nonidentical neurons

On the basis of Hindmarsh-Rose neuron model, dynamical robustness and the transition of firing modes of multilayer memristive neural network consisting of nonidentical neurons have been investigated in detail. The dynamic effects of memristive synapses coupling which are either cubic order flux or quadratic flux are detected. Our results suggest that for the cubic order flux-controlled memristors increasing electromagnetic induction parameter and parameter of memristor show the tendency to spoil the dynamical robustness of the multilayer memristive neural network. For quadratic flux-controlled memristors, weak electromagnetic induction can spoil the dynamical robustness while strong electromagnetic induction and parameter of memristor have little influence on dynamical robustness. We found that the ratio of inactive neurons switches the firing patterns of the active neuron among periodic bursting, chaotic bursting and spiking-like. In the case of memristive synapse coupling by cubic order flux-controlled memristors, chaotic bursting alternates with period bursting as the ratio of inactive neurons is increased, and the chaotic bursting occupy a large range of the ratio of inactive neurons. In the case of memristive synapse coupling by quadratic flux-controlled memristors, the main firing pattern of the active neuron is chaotic bursting. The distribution of interspike interval can be broadly classified into two groups: those that are long interspike intervals and those that are short interspike intervals. The dynamics of multilayer memristive neural network is also verified in the circuits built on Multisim. These results could give new mechanism explanation for aging transition by applying electromagnetic field to neural network.

Rhythmicity and firing modes in modular neuronal network under electromagnetic field

Based on a modified Hindmarsh–Rose model with electromagnetic induction being considered, rhythmicity and firing modes in modular neural network consisting of nonidentical neurons have been explored in detail. The global rhythmicity of the system shows a resonancelike behavior with the increase in the ratio of inactive neurons for strong coupling among neurons inside the subnetwork. We found that interaction between different subnetworks and electromagnetic induction parameter show the tendency to weaken dynamical robustness, whereas self-induction parameter could efficiently improve dynamical robustness of modular network. The dynamics of the active neuron on the road to aging transition is detected. The ratio of inactive neurons switches response-firing modes of the active neuron among spiking, periodic bursting and chaotic bursting. Our model system and results can provide new mechanism explanation for electrical activity in biological systems that are prone to suffer damage or deterioration.

Suppressing the spiking of a synchronized array of Izhikevich neurons

The aim of this research work is to investigate the synchronization and desynchronization of an array of non-identical Izhikevich neurons in a star-like configuration. Both regular spiking neurons and fast spiking neurons are considered in the analysis. The equilibrium points and their stability for a single neuron are determined, and an adaptive stable filter is applied to suppress the spiking of the neuron. A star coupling array configuration is applied to synchronize an array of isolated neurons. Next, the adaptive stable filter is employed to suppress the spiking of the synchronized array of coupled neurons. Appreciably, one filter is enough to suppress the entire star-like array. Numerical simulations demonstrate the success of the proposed technique. The parameters that govern the performance of the filter are specified, the limitations of the methodology are identified, and the required conditions for application are identified.

Coexisting firing patterns and phase synchronization in locally active memristor coupled neurons with HR and FN models

Local activity is regarded as the origin of complexity. In this study, a locally active memristor with coexisting two stable pinched hysteresis loops and two local activity regions is proposed. Its nonvolatile memory, as well as locally active characteristics, is validated by the power-off plot and DC V–I plot. Based on two-dimensional Hindmarsh–Rose and two-dimensional Fitzhugh–Nagumo neurons, a simple neural network is constructed by connecting the two neurons with the locally active memristor. Coexisting multiple firing patterns under different initial conditions are investigated by considering the coupling strength as a unique controlled parameter. The results suggest that the system exhibits coexisting periodic and chaotic bursting firing patterns as well as coexisting two periodic firing patterns with different topologies. Furthermore, state switching without parameters is also explored. In particular, phase synchronization of the memristor synapse-coupled neurons is discussed, which implies that two nonidentical neurons gradually become phase synchronized with the increase in the coupling strength. In order to confirm the effectiveness of numerical simulations, circuit simulations are included.

Circuit Stability to Perturbations Reveals Hidden Variability in the Balance of Intrinsic and Synaptic Conductances.

Neurons and circuits each with a distinct balance of intrinsic and synaptic conductances can generate similar behavior but sometimes respond very differently to perturbation. Examining a large family of circuit models with non-identical neurons and synapses underlying rhythmic behavior, we analyzed the circuits' response to modifications in single and multiple intrinsic conductances in the individual neurons. To summarize these changes over the entire range of perturbed parameters, we quantified circuit output by defining a global stability measure. Using this measure, we identified specific subsets of conductances that when perturbed generate similar behavior in diverse individuals of the population. Our unbiased clustering analysis enabled us to quantify circuit stability when simultaneously perturbing multiple conductances as a nonlinear combination of single conductance perturbations. This revealed surprising conductance combinations that can predict the response to specific perturbations, even when the remaining intrinsic and synaptic conductances are unknown. Therefore, our approach can expose hidden variability in the balance of intrinsic and synaptic conductances of the same neurons across different versions of the same circuit solely from the circuit response to perturbations. Developed for a specific family of model circuits, our quantitative approach to characterizing high-dimensional degenerate systems provides a conceptual and analytic framework to guide future theoretical and experimental studies on degeneracy and robustness.SIGNIFICANCE STATEMENT Neural circuits can generate nearly identical behavior despite neuronal and synaptic parameters varying several-fold between individual instantiations. Yet, when these parameters are perturbed through channel deletions and mutations or environmental disturbances, seemingly identical circuits can respond very differently. What distinguishes inconsequential perturbations that barely alter circuit behavior from disruptive perturbations that drastically disturb circuit output remains unclear. Focusing on a family of rhythmic circuits, we propose a computational approach to reveal hidden variability in the intrinsic and synaptic conductances in seemingly identical circuits based solely on circuit output to different perturbations. We uncover specific conductance combinations that work similarly to maintain stability and predict the effect of changing multiple conductances simultaneously, which often results from neuromodulation or injury.

Mechanism for explosive synchronization of neural networks.

Here we investigate the mechanism for explosive synchronization (ES) of a complex neural network composed of nonidentical neurons and coupled by Newman-Watts small-world matrices. We find a range of nonlocal connection probabilities for which the network displays an abrupt transition to phase synchronization, characterizing ES. The mechanism behind the ES is the following: As the coupling parameter is varied in a network of distinct neurons, ES is likely to occur due to a bistable regime, namely a chaotic nonsynchronized and a regular phase-synchronized state in the phase space. In this case, even small coupling changes make possible a transition between them. The onset of ES occurs via a saddle-node bifurcation of a periodic orbit that leads the network dynamics to display a locally stable phase-synchronized state. The presence of this regime is accompanied by a hysteresis loop on the network dynamics as the coupling parameter is adiabatically increased and decreased. The end of the hysteresis loop is marked by a frontier crisis of the chaotic attractor which also determines the end of the coupling strength interval where ES is possible.

Synchronization of Rulkov neuron networks coupled by excitatory and inhibitory chemical synapses.

This paper takes into account a neuron network model in which the excitatory and the inhibitory Rulkov neurons interact each other through excitatory and inhibitory chemical coupling, respectively. Firstly, for two or more identical or non-identical Rulkov neurons, the existence conditions of the synchronization manifold of the fixed points are investigated, which have received less attention over the past decades. Secondly, the master stability equation of the arbitrarily connected neuron network under the existence conditions of the synchronization manifold is discussed. Thirdly, taking three identical Rulkov neurons as an example, some new results are presented: (1) topological structures that can make the synchronization manifold exist are given, (2) the stability of synchronization when different parameters change is discussed, and (3) the roles of the control parameters, the ratio, as well as the size of the coupling strength and sigmoid function are analyzed. Finally, for the chemical coupling between two non-identical neurons, the transversal system is given and the effect of two coupling strengths on synchronization is analyzed.

Bifurcations and Synchronization of Delay-Coupled Neuronal Networks with Autaptic Connections

This paper focuses on the dynamic behaviors of delay-coupled networks consisting of an arbitrary number of nonidentical neurons with unidirectional connections and an electrical synapse from one neuron onto itself. The stability criteria and different types of bifurcations are discussed by decomposing and analyzing the associated characteristic equation. Then, the study turns to the validation of theoretical results through numerical simulations and various interesting neural activities are observed, such as nontrivial equilibria, different patterns of oscillations, multistability coexistence, multiple switches between the quiescent and different periodic states, and transitions between the coexisting equilibria and the coexistence of equilibria and periodic oscillations. It is shown that time delays play important roles in the system performance and can be used to control neural activities.

Bursting and Synchronization in a Two-Compartment Model with Current-Feedback Control

Based on the fast–slow dynamics and bifurcation analysis, two different types of bursting, that is, the “subHopf/homoclinic” and the “circle/fold cycle” types of bursting, are presented and analyzed in a two-compartment neuron model with current feedback control due to totally different generation mechanisms. The synchronization transition process from burst synchronization to nearly complete synchronization is considered in two electrically coupled nonidentical neurons, and fast–slow analysis can be extended to explore the bursting behavior of nearly complete synchronization. The analysis of bursting types and multitime-scale synchronization transition may help us better understand the information encoding and transmission in neural systems.

Autapse-induced synchronization in a coupled neuronal network

The effect of autapse on coupled neuronal network is detected. In our studies, three identical neurons are connected with ring type and autapse connected to one neuron of the network. The autapse connected to neuron can impose time-delayed feedback in close loop on the neuron thus the dynamics of membrane potentials can be changed. Firstly, the effect of autapse driving on single neuron is confirmed that negative feedback can calm down the neuronal activity while positive feedback can excite the neuronal activity. Secondly, the collective electrical behaviors of neurons are regulated by a pacemaker, which associated with the autapse forcing. By using appropriate gain and time delay in the autapse, the neurons can reach synchronization and the membrane potentials of all neurons can oscillate with the same rhythm under mutual coupling. It indicates that autapse forcing plays an important role in changing the collective electric activities of neuronal network, and appropriate electric modes can be selected due to the switch of feedback type(positive or negative) in autapse. And the autapse-induced synchronization in network is also consistent with some biological experiments about synchronization between nonidentical neurons.

Stability of the synchronized network of Hindmarsh–Rose neuronal models with nearest and global couplings

We analytically and numerically investigate a set of N identical and non-identical Hindmarsh–Rose neuronal models with nearest-neighbor and global couplings. The stability boundary of the synchronized states is analyzed using the Master Stability Function approach for the case of identical oscillators (complete synchronization) and the Kuramoto order parameter for the disordered case (phase synchronization). We find that, through a linear coupling modeling electrical synapses, complete synchronization occurs in a system of many nearest-neighbor or globally coupled identical oscillators, and in the case of non-identical neurons it is stable even in the presence of a spread of the parameters. We find that the Hindmarsh–Rose neuronal models can synchronize when coupled through the action of potential variable or through the interaction by rapid flows of ions through the membrane. The degree of connectivity of the network favors synchronization: in the global coupling case, the threshold for the in-phase state stabilizes when the number of dynamical units increases. The transition from disordered to the ordered state is a second order dynamical phase transition, although very sharp.

Complex dynamics of a delayed discrete neural network of two nonidentical neurons

In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zou [J. Nonlinear Sci. 15, 291-303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415-432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869-1878 (2013)]. We also give some numeric simulations to verify our theoretical results.

Chaotic invariant sets of a delayed discrete neural network of two non-identical neurons

In this paper, we show that a delayed discrete Hopfield neural network of two nonidentical neurons with no self-connections can demonstrate chaotic behavior in a region away from the origin. To this end, we first transform the model, by a novel way, into an equivalent system which enjoys some nice properties. Then, we identify a chaotic invariant set for this system and show that the system within this set is topologically conjugate to the full shift map on two symbols. This confirms chaos in the sense of Devaney. Our main result is complementary to the results in Kaslik and Balint (2008) and Huang and Zou (2005), where it was shown that chaos may occur in neighborhoods of the origin for the same system. We also present some numeric simulations to demonstrate our theoretical results.

SYNCHRONIZATION AND ANTICOHERENCE RESONANCE OF BURSTING NEURONS WITH SPATIALLY CORRELATED NOISE

We investigate synchronization of bursting neurons, caused by spatially correlated noise, consisting of a common Guassian noise and a local one. It is found that the degree of noise-induced synchronization between identical neurons increases with both the noise intensity and noise correlation. As for non-identical neurons, it is demonstrated that the degree of phase synchronization decreases monotonously with the noise intensity for partially correlated noise, but the degree undergoes a minimum with the common noise intensity increasing. An interpretation is provided for the noise-induced synchronization between identical neurons by investigating noise-modulated spike train pattern in a single neuron. In addition, the coherence of spike train is minimized at some noise intensities.