scholarly journals Investigation of Cortical Signal Propagation and the Resulting Spatiotemporal Patterns in Memristor-Based Neuronal Network

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-20
Author(s):  
Ke Ding ◽  
Zahra Rostami ◽  
Sajad Jafari ◽  
Boshra Hatef
Keyword(s):  
Neuronal Network ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Signal Propagation ◽  
Neuronal Model ◽  
Spatiotemporal Patterns ◽  
Excitable Media ◽  
Spatiotemporal Pattern ◽  
Excitable Tissue ◽  
Type Coupling

Complexity is the undeniable part of the natural systems providing them with unique and wonderful capabilities. Memristor is known to be a fundamental block to generate complex behaviors. It also is reported to be able to emulate synaptic long-term plasticity as well as short-term plasticity. Synaptic plasticity is one of the important foundations of learning and memory as the high-order functional properties of the brain. In this study, it is shown that memristive neuronal network can represent plasticity phenomena observed in biological cortical synapses. A network of neuronal units as a two-dimensional excitable tissue is designed with 3-neuron Hopfield neuronal model for the local dynamics of each unit. The results show that the lattice supports spatiotemporal pattern formation without supervision. It is found that memristor-type coupling is more noticeable against resistor-type coupling, while determining the excitable tissue switch over different complex behaviors. The stability of the resulting spatiotemporal patterns against noise is studied as well. Finally, the bifurcation analysis is carried out for variation of memristor effect. Our study reveals that the spatiotemporal electrical activity of the tissue concurs with the bifurcation analysis. It is shown that the memristor coupling intensities, by which the system undergoes periodic behavior, prevent the tissue from holding wave propagation. Besides, the chaotic behavior in bifurcation diagram corresponds to turbulent spatiotemporal behavior of the tissue. Moreover, we found that the excitable media are very sensitive to noise impact when the neurons are set close to their bifurcation point, so that the respective spatiotemporal pattern is not stable.

scholarly journals Delayed global feedback in the genesis and stability of spatiotemporal patterns in paced biological excitable media

2020 ◽  
Author(s):  
Zhen Song ◽  
Zhilin Qu
Keyword(s):  
Pattern Formation ◽  
Calcium Release ◽  
Spatiotemporal Dynamics ◽  
Spatiotemporal Patterns ◽  
Excitable Media ◽  
Spatiotemporal Pattern ◽  
Generic Model ◽  
Multi Scale ◽  
Pattern Dynamics ◽  
Period 2

AbstractA multi-scale approach was used to investigate the roles of delayed global feedback (DGF) in the genesis and stability of spatiotemporal patterns in periodically-paced excitable media. Patterns that are temporal period-2 (P2) and spatially concordant (in-phase) or discordant (out-of-phase) were investigated. First, simulations were carried out using a generic spatiotemporal model composed of coupled FitzHugh-Nagumo units with DGF. When DGF is absent, concordant and discordant P2 patterns occur depending on initial conditions. The discordant P2 patterns are spatially random. When the DGF is negative, only concordant P2 patterns exist. When the DGF is positive, both concordant and discordant P2 patterns can occur. The discordant P2 patterns are still spatially random, but they satisfy that the global signal exhibits a temporal period-1 behavior. Second, to validate the spatiotemporal dynamics in a biological system, simulations were carried out using a 3-dimensional physiologically detailed ventricular myocyte model. This model can well capture the intracellular calcium release patterns widely observed in experiments. The properties of DGF were altered by changing ionic currents or clamping voltage. The spatiotemporal pattern dynamics of calcium release in this model match precisely with those of the generic model. Finally, theoretical analyses were carried out using a coupled map lattice model with DGF, which reveals the instabilities and bifurcations leading to the spatiotemporal dynamics and provides a general mechanistic understanding of the role of DGF in the genesis, selection, and stability of spatiotemporal patterns in paced excitable media.Author SummaryUnderstanding the mechanisms of pattern formation in biological systems is of great importance. Here we investigate the dynamical mechanisms by which delayed global feedback affects pattern formation and stability in periodically-paced biological excitable media, such as cardiac or neural cells and tissue. We focus on the formation and stability of the temporal period-2 and spatially in-phase and out-of-phase patterns. Using a multi-scale modeling approach, we show that when the delayed global feedback is negative, only the spatially in-phase patterns are stable; when the feedback is positive, both spatially in-phase and out-of-phase patterns are stable. Also, under the positive feedback, the out-of-phase patterns are spatially random but satisfy that the global signals are temporal period-1 solutions.

scholarly journals Spatiotemporal Patterns Formed by a Discrete Nutrient-Phytoplankton Model with Time Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Feifan Zhang ◽  
Wenjiao Zhou ◽  
Lei Yao ◽  
Xuanwen Wu ◽  
Huayong Zhang
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Numerical Simulations ◽  
Functional Response ◽  
Bifurcation Analysis ◽  
Discrete Model ◽  
Continuous Model ◽  
Spatiotemporal Patterns ◽  
Homogeneous Steady State ◽  
Simulation Results

In this research, a continuous nutrient-phytoplankton model with time delay and Michaelis–Menten functional response is discretized to a spatiotemporal discrete model. Around the homogeneous steady state of the discrete model, Neimark–Sacker bifurcation and Turing bifurcation analysis are investigated. Based on the bifurcation analysis, numerical simulations are carried out on the formation of spatiotemporal patterns. Simulation results show that the diffusion of phytoplankton and nutrients can induce the formation of Turing-like patterns, while time delay can also induce the formation of cloud-like pattern by Neimark–Sacker bifurcation. Compared with the results generated by the continuous model, more types of patterns are obtained and are compared with real observed patterns.

SYNCHRONIZATION PHENOMENA IN NETWORKS OF COUPLED RELAXATION ELECTROCHEMICAL OSCILLATIONS

2006 ◽  
Vol 16 (07) ◽  
pp. 1951-1960 ◽  
Author(s):  
ANTONIS KARANTONIS ◽  
MICHAEL PAGITSAS ◽  
YASUYUKI MIYAKITA ◽  
SEIICHIRO NAKABAYASHI
Keyword(s):  
Laser Pulse ◽  
Phase Relation ◽  
Spatiotemporal Patterns ◽  
Spatiotemporal Pattern ◽  
Network Geometry ◽  
Weakly Coupled

Networks of weakly coupled discrete electrochemical oscillators have the ability of synchronizing rapidly in-phase or out-of-phase, depending on the network geometry. It is shown that a network consisting of N relaxation electrochemical oscillators, coupled through inhibitory connections, can have (N - 1)! coexisting out-of-phase states, each state being a permutation of a periodic spiking sequence. The out-of-phase states can be modified by shots of laser pulse perturbations and the phase relation is stored as a coded spatiotemporal pattern. The ability of the network to function as a re-writable memory of (N - 1)! different spatiotemporal patterns is demonstrated experimentally for N = 4.

BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR

1993 ◽  
Vol 03 (02) ◽  
pp. 399-404 ◽  
Author(s):  
T. SÜNNER ◽  
H. SAUERMANN
Keyword(s):  
Bifurcation Diagram ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Global Bifurcation ◽  
Dynamical Behaviour ◽  
Van Der Pol Oscillator ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Dimensional Models

Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.

Mechanism of dynamic phase transition and synchronous stability in Hindmarsh–Rose neuronal network

2018 ◽  
Vol 32 (28) ◽  
pp. 1850308
Author(s):  
Shi-Dong Liang ◽  
Haoqi Li ◽  
Yuefan Deng
Keyword(s):  
Phase Transition ◽  
Parameter Space ◽  
Lyapunov Stability ◽  
Neuronal Network ◽  
Neuronal Model ◽  
Index Formula ◽  
Neuronal Dynamics ◽  
Dynamical Phase ◽  
Dynamic Phase ◽  
Dynamic Phase Transition

The neuronal dynamics plays an important role in understanding the neurological phenomena. We study the mechanism of the dynamic phase transition and its Lyapunov stability of a single Hindmarsh–Rose (HR) neuronal model. We propose an index [Formula: see text] to express the dynamical phase of the HR neurons. When [Formula: see text] the neuron is in the pure resting state, and when [Formula: see text] the neuron closes to the pure spiking phase, while when [Formula: see text] the neuron runs in the bursting phase. Based on this method, we investigate numerically the phase diagram of the HR neuronal model in the parameter space. We find that two mechanisms governed the HR neuronal dynamic phase transition, the phase transition and crossover transition in the different regions of the parameter space. Moreover, we analyze the equilibrium point stability of the HR neuronal model based on the Lyapunov stability method. We study the synchronous stability of the HR neuronal network based on the master stability function method and give the phase diagrams of the maximum Lyapunov exponents in the parameter space of networks. The regions of the synchronous stabilities in the parameter space depend on the couplings of the HR neurons of the membrane potential and the flux of the fast ion channel between the HR neurons. These results help to understand the HR neuronal dynamics and the synchronous stability of the HR neuronal networks.

scholarly journals Propagating Wave and Irregular Dynamics: Spatiotemporal Patterns of Cholinergic Theta Oscillations in Neocortex In Vitro

2003 ◽  
Vol 90 (1) ◽  
pp. 333-341 ◽  
Author(s):  
Weili Bao ◽  
Jian-Young Wu
Keyword(s):  
Phase Distribution ◽  
Signal To Noise Ratio ◽  
Human Subjects ◽  
Local Oscillator ◽  
Spatiotemporal Patterns ◽  
Spatiotemporal Pattern ◽  
Large Signal ◽  
Local Oscillators ◽  
Theta Oscillation

Neocortical “theta” oscillation (5–12 Hz) has been observed in animals and human subjects but little is known about how the oscillation is organized in the cortical intrinsic networks. Here we use voltage-sensitive dye and optical imaging to study a carbachol/bicuculline induced theta (∼8 Hz) oscillation in rat neocortical slices. The imaging has large signal-to-noise ratio, allowing us to map the phase distribution over the neocortical tissue during the oscillation. The oscillation was organized as spontaneous epochs and each epoch was composed of a “first spike,” a “regular” period (with relatively stable frequency and amplitude), and an “irregular” period (with variable frequency and amplitude) of oscillations. During each cycle of the regular oscillation, one wave of activation propagated horizontally (parallel to the cortical lamina) across the cortical section at a velocity of ∼50 mm/s. Vertically the activity was synchronized through all cortical layers. This pattern of one propagating wave associated with one oscillation cycle was seen during all the regular cycles. The oscillation frequency varied noticeably at two neighboring horizontal locations (330 μm apart), suggesting that the oscillation is locally organized and each local oscillator is about ≤300 μm wide horizontally. During irregular oscillations, the spatiotemporal patterns were complex and sometimes the vertical synchronization decomposed, suggesting a de-coupling among local oscillators. Our data suggested that neocortical theta oscillation is sustained by multiple local oscillators. The coupling regime among the oscillators may determine the spatiotemporal pattern and switching between propagating waves and irregular patterns.

scholarly journals Delay-induced synchronization transition in a small-world neuronal network of FitzHugh–Nagumo neurons subjected to sine-Wiener bounded noise

2019 ◽  
Vol 33 (08) ◽  
pp. 1950053 ◽  
Author(s):  
Yuangen Yao ◽  
Ming Yi ◽  
Dejia Hou
Keyword(s):  
Neuronal Network ◽  
Correlation Time ◽  
Small World ◽  
Nearest Neighbors ◽  
Spatiotemporal Patterns ◽  
Small World Network ◽  
Bounded Noise ◽  
Future Studies ◽  
Synchronization Transition ◽  
Brain Functions

Noise and delay are ubiquitous in brain and they have significant effects on neuronal network synchronization and even brain functions. Based on a small-world neuronal network of delayed FitzHugh–Nagumo (FHN) neurons subjected to sine-Wiener (SW) bounded noise, the effects of delay and SW noise on synchronization and synchronization transition are numerically investigated by calculating a synchronization measure R and plotting spatiotemporal patterns. The phenomenon of delay-induced synchronization transition is observed as delay [Formula: see text] is increased. And large self-correlation time and strength of SW noise can increase the number of delay-induced synchronization transition. In addition, delay-induced synchronization transition is robust against the change of topology structure of neuronal network and this phenomenon becomes much easier to see for small nearest neighbors k in the small-world network. Since synchronization transition may imply functional switch, our results may have important implications, and inspire future studies.

Breakup of spatiotemporal pattern under electromagnetic radiation

2019 ◽  
Vol 33 (16) ◽  
pp. 1950165 ◽  
Author(s):  
Fan Li ◽  
Linwei Guo
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Radiation ◽  
Cardiac Tissue ◽  
Signal Propagation ◽  
Spatiotemporal Pattern ◽  
Quiescent State ◽  
Wave Source ◽  
The Media ◽  
Electrical Activities ◽  
Target Wave

Stable wave propagation is important for heart health, however, the electromagnetic radiation could affect normal signal propagation of heart, even make a sudden cardiac arrest. In this paper, the effect of electromagnetic radiation on the propagation of stable target wave generated by linear feedback control is studied in detail. It is confirmed that there are different transitions of electrical activities in cardiac tissue, which are transitions from target wave to spiral wave, some isolated islands of pattern waves coexisted, broken pattern and even the quiescent state, are generated when the electromagnetic field is imposed on the cardiac tissue in three ways. Furthermore, it is interesting to find there are different real affected regions, in which the electrical activities of nodes are destroyed, when the radiation signal is imposed on the cardiac tissue in different ways. It is also found the kinds of dynamical behaviors in the media are dependent on the real affected region. These results state that electromagnetic radiation could change the electrical activities, even destroy and suppress the wave propagation of wave source, and the ways of electromagnetic radiation imposed on the media are also important.

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