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 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.

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.

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.

Study on the Hamilton Dynamical System of Wheel-and-Rail Dynamical Model of High-Speed Train

2015 ◽  
Vol 713-715 ◽  
pp. 99-102
Author(s):  
Hong Yun Shen ◽  
Jian Hua Du ◽  
Yu Lin Wang
Keyword(s):  
Dynamical System ◽  
Dry Friction ◽  
High Speed ◽  
Dynamical Model ◽  
High Speed Train ◽  
Damping Force ◽  
Nonlinear Dynamical ◽  
Dynamical Behaviors ◽  
Practical Engineering

The study on dynamical model of wheel and rail of high-speed train has attracted many researchers nowadays. According to the damping force and the dry friction between wheel and rail, the dynamical model of wheel and rail of high-speed train is constructed and the Hamilton dynamical system of this model is analyzed to discuss its nonlinear dynamical behaviors, which will benefit the practical engineering of high-speed train.

scholarly journals The frustrated brain: from dynamics on motifs to communities and networks

2014 ◽  
Vol 369 (1653) ◽  
pp. 20130532 ◽  
Author(s):  
Leonardo L. Gollo ◽  
Michael Breakspear
Keyword(s):  
Cognitive Processes ◽  
Large Scale ◽  
Phase Synchronization ◽  
Metastable Phase ◽  
Network Size ◽  
Stable States ◽  
Adaptive Function ◽  
Cortical Networks ◽  
Broad Variety ◽  
Coupling Strengths

Cognitive function depends on an adaptive balance between flexible dynamics and integrative processes in distributed cortical networks. Patterns of zero-lag synchrony likely underpin numerous perceptual and cognitive functions. Synchronization fulfils integration by reducing entropy, while adaptive function mandates that a broad variety of stable states be readily accessible. Here, we elucidate two complementary influences on patterns of zero-lag synchrony that derive from basic properties of brain networks. First, mutually coupled pairs of neuronal subsystems—resonance pairs—promote stable zero-lag synchrony among the small motifs in which they are embedded, and whose effects can propagate along connected chains. Second, frustrated closed-loop motifs disrupt synchronous dynamics, enabling metastable configurations of zero-lag synchrony to coexist. We document these two complementary influences in small motifs and illustrate how these effects underpin stable versus metastable phase-synchronization patterns in prototypical modular networks and in large-scale cortical networks of the macaque (CoCoMac). We find that the variability of synchronization patterns depends on the inter-node time delay, increases with the network size and is maximized for intermediate coupling strengths. We hypothesize that the dialectic influences of resonance versus frustration may form a dynamic substrate for flexible neuronal integration, an essential platform across diverse cognitive processes.

Steps in the development of chemical and electrical synapses by pairs of identified leech neurons in culture

1989 ◽  
Vol 236 (1284) ◽  
pp. 253-268 ◽  
Keyword(s):  
Synaptic Transmission ◽  
Electrical Coupling ◽  
The Other ◽  
Enzyme Treatment ◽  
Sensory Cells ◽  
Electrical Transmission ◽  
Retzius Cells ◽  
Chemical Synapses ◽  
P Cells ◽  
Chemical Transmission

Experiments have been made to follow the development of chemical and electrical transmission between pairs of leech neurons in culture. 1. The cell bodies of identified neurons were isolated from the CNS by suction after mild enzyme treatment, together with a length of the initial segment (or ‘stump’). The neurons tested were Retzius cells (R), annulus erector motoneurons (AE), Anterior pagoda cells (AP) and pressure sensory cells (P). Pairs of cells were placed together in various configurations, with different sites on their surfaces making contact. 2. When pairs of Retzius cells were apposed with their stumps touching, serotonergic, chemically mediated synaptic transmission became apparent before electrical transmission. By 2.5 h impulses in either of the two Retzius cells produced hyperpolarizing inhibitory potentials in the other. These potentials were reversed by raised intracellular CI and showed clear facilitation. The strength of chemical transmission between Retzius cells increased over the next 72 h. 3. After chemical transmission had been established, weak non-recti­fying electrical transmission became apparent between Retzius cells at about 24–72 h. By 4 days coupling became stronger and tended to obscure chemically evoked synaptic potentials. 4. When pairs of Retzius cells were aligned in culture with the tip of one cell stump touching the soma of the other, chemical transmission also developed rapidly. Transmission was, however, in one direction, from stump to soma. At later stages non-rectifying electrical coupling devel­oped as with stump-stump configuration. With the cell bodies of two Retzius cells apposed, electrical coupling developed after several days, before chemical transmission could be observed. 5. When Retzius and P cells were cultured with their stumps in con­tact, inhibitory chemical synaptic transmission developed within 24 h. Transmission was always in one direction, from Retzius to P cell. Electrical coupling of Retzius and P cells never occurred whatever the spatial relations of the cells to one another. 6. Annulus erector motoneurons, which contain ACh and a peptide resembling FMRFamide, first developed electrical coupling when the two stumps were in contact and then, later, bi-directional chemical transmission. Anterior Pagoda pairs placed stump-to-stump showed electrical connections. 7. Electronmicrographs revealed the presence of synaptic structures within24 h after Retzius-Retzius, Retzius-P or AE–AE stumps were apposed. 8. The specificity of connections between cultured cells was similar to that observed in earlier experiments. A marked difference was in the speed and reliability with which chemical synapses developed when stumps were in contact. The results show that the tip of a neuron represents a preferential site for the formation of chemical synapses.

Flow Induced Dynamics of Plate Seals

2019 ◽  
Author(s):  
Deepak Trivedi ◽  
Bernardo Kerr
Keyword(s):  
High Speed ◽  
Phase Locking ◽  
Flow Analysis ◽  
Feedback Mechanism ◽  
Experimental Methodology ◽  
Dynamical Instability ◽  
Amplitude Death ◽  
Flow Induced Vibration ◽  
Center Manifold Reduction ◽  
Pressure Drops

Abstract Plate seals can provide low leakage at rotor-stator interfaces with large pressure drops in turbomachinery within a limited axial span. When designed with a self-correcting hydrostatic feedback mechanism, non-contact operation could be achieved even in the presence of large rotor transients. Flow induced dynamical instability is one of the key design challenges in plate seals for rotor-stator sealing in turbomachinery. The instabilities are caused by potentially multiple flow induced vibration mechanisms operating during different flow regimes. This paper investigates mechanisms of vortex induced flutter in compliant plate seals, which happens when the vortex shedding frequency of the plates comes close to one of the natural frequencies of vibration of the structure. An experimental methodology based on optical flow analysis of high speed videography is proposed to characterize vibrations of the ensemble of plates (“leafpack”.) Experiments show that the compliant plates vibrate in the flow field with amplitude dependent on the pressure drop. Additionally, the vibrations of individual plates are highly coupled to each other, leading to phase-locking or phase-drifting depending on boundary conditions. The leafpack has a characteristic frequency and exhibits traveling wave phenomena under certain conditions of pressurization. Using experimental insights, plate seals are modeled as a ring of a large (∼103) number of locally coupled oscillators, with nonlinear stiffness arising from hydrostatic forces. A two-way coupling exists between the structural and fluid wake dynamics. Using center manifold reduction, the coupled fourth order dynamics of the system is reduced to second order and transform the equations into the normal form for investigating the possibility of mitigating flow induced vibrations through the phenomenon of amplitude death. Conditions under which successful induction of amplitude death could eliminate plate vibration in the mode under consideration is discussed.

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.

Sign in / Sign up

Export Citation Format

Share Document