scholarly journals A New Memristive Neuron Map Model and Its Network’s Dynamics under Electrochemical Coupling

Electronics ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 153
Author(s):  
Balamurali Ramakrishnan ◽  
Mahtab Mehrabbeik ◽  
Fatemeh Parastesh ◽  
Karthikeyan Rajagopal ◽  
Sajad Jafari
Keyword(s):  
Cluster Synchronization ◽  
Ring Network ◽  
Complete Synchronization ◽  
Neuron Models ◽  
Circuit Element ◽  
Chaotic Bursting ◽  
Chemical Coupling ◽  
Coupling Strengths ◽  
Electrochemical Coupling ◽  
Chemical Synapses

A memristor is a vital circuit element that can mimic biological synapses. This paper proposes the memristive version of a recently proposed map neuron model based on the phase space. The dynamic of the memristive map model is investigated by using bifurcation and Lyapunov exponents’ diagrams. The results prove that the memristive map can present different behaviors such as spiking, periodic bursting, and chaotic bursting. Then, a ring network is constructed by hybrid electrical and chemical synapses, and the memristive neuron models are used to describe the nodes. The collective behavior of the network is studied. It is observed that chemical coupling plays a crucial role in synchronization. Different kinds of synchronization, such as imperfect synchronization, complete synchronization, solitary state, two-cluster synchronization, chimera, and nonstationary chimera, are identified by varying the coupling strengths.

scholarly journals Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps

2021 ◽  
Vol 18 (6) ◽  
pp. 9394-9409
Author(s):  
Mahtab Mehrabbeik ◽  
◽  
Fatemeh Parastesh ◽  
Janarthanan Ramadoss ◽  
Karthikeyan Rajagopal ◽  
...  
Keyword(s):  
High Speed ◽  
Phase Synchronization ◽  
Electrical Coupling ◽  
Amplitude Death ◽  
Collective Behaviors ◽  
Chimera State ◽  
Dynamical Behaviors ◽  
Chemical Coupling ◽  
Coupling Strengths ◽  
Chemical Synapses

<abstract> <p>Map-based neuronal models have received much attention due to their high speed, efficiency, flexibility, and simplicity. Therefore, they are suitable for investigating different dynamical behaviors in neuronal networks, which is one of the recent hottest topics. Recently, the memristive version of the Rulkov model, known as the m-Rulkov model, has been introduced. This paper investigates the network of the memristive version of the Rulkov neuron map to study the effect of the memristor on collective behaviors. Firstly, two m-Rulkov neuronal models are coupled in different cases, through electrical synapses, chemical synapses, and both electrical and chemical synapses. The results show that two electrically coupled memristive neurons can become synchronous, while the previous studies have shown that two non-memristive Rulkov neurons do not synchronize when they are coupled electrically. In contrast, chemical coupling does not lead to synchronization; instead, two neurons reach the same resting state. However, the presence of both types of couplings results in synchronization. The same investigations are carried out for a network of 100 m-Rulkov models locating in a ring topology. Different firing patterns, such as synchronization, lagged-phase synchronization, amplitude death, non-stationary chimera state, and traveling chimera state, are observed for various electrical and chemical coupling strengths. Furthermore, the synchronization of neurons in the electrical coupling relies on the network's size and disappears with increasing the nodes number.</p> </abstract>

scholarly journals Mechanisms Underlying Fictive Feeding in Aplysia: Coupling Between a Large Neuron With Plateau Potentials Activity and a Spiking Neuron

2002 ◽  
Vol 87 (5) ◽  
pp. 2307-2323 ◽  
Author(s):  
Abraham J. Susswein ◽  
Itay Hurwitz ◽  
Richard Thorne ◽  
John H. Byrne ◽  
Douglas A. Baxter
Keyword(s):  
Computational Models ◽  
Extended Period ◽  
Excitatory Postsynaptic Potential ◽  
Rhythmic Movements ◽  
Buccal Ganglia ◽  
Stochastic Fluctuations ◽  
Slow Kinetics ◽  
Chemical Coupling ◽  
Simulated Network ◽  
Chemical Synapses

The buccal ganglia of Aplysia contain a central pattern generator (CPG) that organizes the rhythmic movements of the radula and buccal mass during feeding. Many of the cellular and synaptic elements of this CPG have been identified and characterized. However, the roles that specific cellular and synaptic properties play in generating patterns of activity are not well understood. To examine these issues, the present study developed computational models of a portion of this CPG and used simulations to investigate processes underlying the initiation of patterned activity. Simulations were done with the SNNAP software package. The simulated network contained two neurons, B31/B32 and B63. The development of the model was guided and constrained by the available current-clamp data that describe the properties of these two protraction-phase interneurons B31/B32 and B63, which are coupled via electrical and chemical synapses. Several configurations of the model were examined. In one configuration, a fast excitatory postsynaptic potential (EPSP) from B63 to B31/B32 was implemented in combination with an endogenous plateau-like potential in B31/B32. In a second configuration, the excitatory synaptic connection from B63 to B31/B32 produced both fast and slow EPSPs in B31/B32 and the plateau-like potential was removed from B31/B32. Simulations indicated that the former configuration (i.e., electrical and fast chemical coupling in combination with a plateau-like potential) gave rise to a circuit that was robust to changes in parameter values and stochastic fluctuations, that closely mimicked empirical observations, and that was extremely sensitive to inputs controlling the onset of a burst. The coupling between the two simulated neurons served to amplify exogenous depolarizations via a positive feedback loop and the subthreshold activation of the plateau-like potential. Once a burst was initiated, the circuit produced the program in an all-or-none fashion. The slow kinetics of the simulated plateau-like potential played important roles in both initiating and maintaining the burst activity. Thus the present study identified cellular and network properties that contribute to the ability of the simulated network to integrate information over an extended period before a decision is made to initiate a burst of activity and suggests that similar mechanisms may operate in the buccal ganglia in initiating feeding movements.

Synchronization or cluster synchronization in coupled Van der Pol oscillators networks with different topological types

2021 ◽  
Author(s):  
Shuai Wang ◽  
Yong Li
Keyword(s):  
Periodic Solutions ◽  
Phase Synchronization ◽  
Van Der Pol Oscillator ◽  
Cluster Synchronization ◽  
Critical Conditions ◽  
Complete Synchronization ◽  
Van Der Pol ◽  
Special Groups ◽  
Different Types ◽  
Van Der Pol Oscillators

Abstract In this paper, we try to discuss the mechanism of synchronization or cluster synchronization in the coupled Van der Pol oscillator networks with different topology types by using the theory of rotating periodic solutions. The synchronous solutions here are transformed into rotating periodic solutions of some dynamical systems. By analyzing the bifurcation of rotating periodic solutions, the critical conditions of synchronous solutions are given in three different networks. We use the rotating periodic matrix in the rotating periodic theory to judge various types of synchronization phenomena, such as complete synchronization, anti-phase synchronization, periodic synchronization, or cluster synchronization. All rotating periodic matrices which satisfy the exchange invariance of multiple oscillators form special groups in these networks. By using the conjugate classes of these groups, we obtain various possible synchronization solutions in the three networks. In particular, we find symmetry has different effects on synchronization in different networks. The network with better symmetry has more elements in the corresponding group, which may have more types of synchronous solutions. However, different types of symmetry may get the same type of synchronous solutions or different types of synchronous solutions, depending on whether their corresponding rotating periodic matrices are similar.

EFFECTS OF UNILATERAL COUPLING BETWEEN TWO CHAOTIC X-BAND GUNN OSCILLATORS

2013 ◽  
Vol 23 (11) ◽  
pp. 1350185 ◽  
Author(s):  
B. C. SARKAR ◽  
S. SARKAR ◽  
C. KOLEY ◽  
A. K. GUIN ◽  
T. BANERJEE
Keyword(s):  
Numerical Simulation ◽  
System Approach ◽  
Design Parameters ◽  
Generalized Synchronization ◽  
Chaotic Oscillations ◽  
Complete Synchronization ◽  
X Band ◽  
Coupling Strengths ◽  
Dc Bias ◽  
Gunn Oscillators

Two X-band microwave Gunn oscillators have been separately operated with "below threshold" dc bias voltages under the influence of an injected weak RF field in their respective cavities to generate chaotic oscillations. The output of one such chaotic Gunn oscillator is injected into the other through a controllable coupling network to explore the possibility of synchronization between two oscillators. We establish through numerical simulation that (i) two oscillators with identical design parameters attain a state of complete synchronization and (ii) two oscillators with slightly different design parameters attain a state of generalized synchronization for reasonable value of coupling strengths. The occurrence of generalized synchronization has been proved through the "auxiliary" slave system approach of nonlinear analysis. Results of hardware experiments are incorporated to qualitatively support the observations made through numerical simulation.

The complete synchronization of coupled Morris–Lecar neurons with chemical synapses

2016 ◽  
Vol 30 (17) ◽  
pp. 1650096 ◽  
Author(s):  
Guanping Wang ◽  
Wuyin Jin ◽  
An Wang
Keyword(s):  
Lyapunov Function ◽  
Stability Theory ◽  
Analytical Approach ◽  
Model Solution ◽  
Sufficient Condition ◽  
Neuronal System ◽  
Complete Synchronization ◽  
Basic Principles ◽  
Chemical Synapses

Based on the basic principles of stability theory and Lyapunov function, the condition of complete synchronization in coupled Morris–Lecar (ML) neuronal system with chemical synapses is studied in this work. The boundedness of the model solution is proved by analytical approach, the sufficient condition of the complete synchronization is proposed based on the quadratic of the constructed Lyapunov function and the result is verified by simulations.

Nonsynaptic modulation of neuronal activity in the brain: electric currents and extracellular ions

1995 ◽  
Vol 75 (4) ◽  
pp. 689-723 ◽  
Author(s):  
J. G. Jefferys
Keyword(s):  
Electric Fields ◽  
Neuronal Activity ◽  
Neuronal Excitability ◽  
Physiological Activity ◽  
Electrical Coupling ◽  
Epileptic Seizures ◽  
Mammalian Brain ◽  
Chemical Coupling ◽  
Extracellular Ions ◽  
Chemical Synapses

Nonsynaptic interactions between neurons have been eclipsed by our increasingly detailed understanding of chemical synapses, but they do play significant roles in the nervous system. This review considers four classes of nonsynaptic interaction, mainly in mammalian brain. 1) Electrotonic (and chemical) coupling through gap junctions has effects during development and under some, often pathological, conditions in the mature brain. 2) Ephaptic transmission is mediated by electrical coupling between specific neuronal elements in the absence of specialized contacts, notably in the cerebellum, and in axon tracts affected by demyelination. 3) Field effect interactions are mediated by large extracellular currents and potential fields generated by the hippocampus and other cortical structures. Both endogenous and applied electric fields alter neuronal excitability at field strengths over a few millivolts per millimeter. Weaker fields have more subtle effects, for instance, on axonal growth during development and repair and, more controversially, in behavioral responses to environmental fields. 4) There are fluctuations in extracellular ions such as K+, which are released during neuronal activity and which alter neuronal excitability. Field effects and ion fluctuations probably have modest effects during physiological activity but have a significant impact on epileptic seizures, and can sustain them in the absence of synaptic transmission.

Transition of synchronization of coupled maps in modular networks

2019 ◽  
Vol 31 (01) ◽  
pp. 2050011
Author(s):  
Bin Zhang ◽  
Ru-Hai Du ◽  
Sheng-Jun Wang ◽  
Shi-Xian Qu
Keyword(s):  
Coupling Strength ◽  
Phase Synchronization ◽  
Spatiotemporal Chaos ◽  
Spatiotemporal Patterns ◽  
Cluster Synchronization ◽  
Complete Synchronization ◽  
Modular Networks ◽  
Fully Connected ◽  
Fully Connected Networks ◽  
Ordered State

Spatiotemporal patterns in the transition of phase synchronization in modular networks of coupled logistic maps are studied. The phase diagram of spatiotemporal patterns is presented by analyzing both the collective behavior of direction-phase and the changes of links connecting clusters of different phases. The spatiotemporal chaos is obtained when the coupling strength is weak. We show that the spatiotemporal chaos can be composed by clusters in periodic states. The region of periodic behaviors is independent of modularity. Then with decreasing coupling or increasing modularity, the system presents the same transition path from complete synchronization to cluster synchronization, except the network is close to fully connected networks. There are two distinctive scenarios from disordered behavior to an ordered state when the modularity ratio varies from one to zero. First, for networks with small modularity, the number of phase synchronized clusters decreases with the increasing of the coupling strength. Second, for networks with large modularity, the number of phase-synchronized clusters nonmonotonically changes with the coupling strength.

scholarly journals CLUSTER SYNCHRONIZATION IN THREE-DIMENSIONAL LATTICES OF DIFFUSIVELY COUPLED OSCILLATORS

2003 ◽  
Vol 13 (04) ◽  
pp. 755-779 ◽  
Author(s):  
VLADIMIR N. BELYKH ◽  
IGOR V. BELYKH ◽  
MARTIN HASLER ◽  
KONSTANTIN V. NEVIDIN
Keyword(s):  
Coupled Oscillators ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Cluster Synchronization ◽  
Global Synchronization ◽  
Lur’E Systems ◽  
Coupling Strengths ◽  
Linear Invariant ◽  
The Stability

Cluster synchronization modes of continuous time oscillators that are diffusively coupled in a three-dimensional (3-D) lattice are studied in the paper via the corresponding linear invariant manifolds. Depending in an essential way on the number of oscillators composing the lattice in three volume directions, the set of possible regimes of spatiotemporal synchronization is examined. Sufficient conditions of the stability of cluster synchronization are obtained analytically for a wide class of coupled dynamical systems with complicated individual behavior. Dependence of the necessary coupling strengths for the onset of global synchronization on the number of oscillators in each lattice direction is discussed and an approximative formula is proposed. The appearance and order of stabilization of the cluster synchronization modes with increasing coupling between the oscillators are revealed for 2-D and 3-D lattices of coupled Lur'e systems and of coupled Rössler oscillators.

Effect of Delay on the Synchronization of Weakly Coupled Neurons via Inhibitory Chemical Synapses

2014 ◽  
Vol 519-520 ◽  
pp. 846-849
Author(s):  
Rui Xue Li ◽  
Yan Qiu Che ◽  
Ping Hao ◽  
Xiao Qin Li
Keyword(s):  
Phase Synchronization ◽  
Phase Model ◽  
Neuronal System ◽  
Neuronal Dynamics ◽  
Emergent Phenomena ◽  
Weakly Coupled ◽  
Chemical Coupling ◽  
Simple Phase ◽  
Chemical Synapses ◽  
The Stability

Inhibitory chemical coupling connections are ubiquitous in neuronal system. In this paper, we first reduce the complex neuronal dynamics to a simple phase model by means of phase-model reduction method. Then we examine the roles of time delays extensively on the synchronization properties by bifurcation analysis and numerical simulation. Finally, we identify the existence and the stability of various phase-locked states. Along with the expected phase and anti-phase synchronization regimes, we find the emergent phenomena that significantly influence the synchronization behavior.

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