The electric activity of neuron and collective behaviors of neurons can be modulated by autapse, which can be described by self-feedback current in close loop with time delay being considered. Distribution of electric autapses in a local area can introduce heterogeneity in the network and thus traveling wave emits from this area. In this paper, diversity in time delay of electric autapse is considered and collision between emitting waves from different local areas driven by electric autapses under different time delays is observed. In the numerical studies, neurons in the square area with 15×15 (and/or 20×20) nodes are connected electric autapses with different time delays and target-like waves are induced and converted into, spiral waves after continuous collision between wave fronts. It is found that a group of spiral waves can emerge in the network, or coexist with target waves under appropriate coupling intensity due to time delay diversity in autapse and these waves can regulate the collective behaviors of neurons as continuous pacemakers.

Pattern selection in neuronal network driven by electric autapses with diversity in time delays

Synapse coupling can benefit signal exchange between neurons and information encoding for neurons, and the collective behaviors such as synchronization and pattern selection in neuronal network are often discussed under chemical or electric synapse coupling. Electromagnetic induction is considered at molecular level when ion currents flow across the membrane and the ion concentration is fluctuated. Magnetic flux describes the effect of time-varying electromagnetic field, and memristor bridges the membrane potential and magnetic flux according to the dimensionalization requirement. Indeed, field coupling can contribute to the signal exchange between neurons by triggering superposition of electric field when synapse coupling is not available. A chain network is designed to investigate the modulation of field coupling on the collective behaviors in neuronal network connected by electric synapse between adjacent neurons. In the chain network, the contribution of field coupling from each neuron is described by introducing appropriate weight dependent on the position distance between two neurons. Statistical factor of synchronization is calculated by changing the external stimulus and weight of field coupling. It is found that the synchronization degree is dependent on the coupling intensity and weight, the synchronization, pattern selection of network connected with gap junction can be modulated by field coupling.

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Collective responses in electrical activities of neurons under field coupling.

Pattern estimation and selection in media can give important clues to understand the collective response to external stimulus by detecting the observable variables. Both reaction–diffusion systems ...

A review and guidance for pattern selection in spatiotemporal system

27p-PS-136 Spiral Breakup in a New Model of Discrete Excitable Media

In this paper, a certain kind of intermittent scheme is used to control the chaos in a single chaotic Chua circuit to reach an arbitrary orbit. Furthermore, it is confirmed to be effective in suppressing spatiotemporal chaos and a spiral wave in the networks of Chua circuits with nearest-neighbor connections. The controllable and measurable variable is sampled, and the linear error between the sampled variable and the selected thresholds is fed back into the system only if the sampled variable exceeds the thresholds; otherwise, the system will develop itself without any external perturbation. In experiments, the control scheme could be realized by using the Heavside function. In the case of one single chaotic Chua circuit, the chaotic state can be controlled to reach an arbitrary n-periodical orbit (n=1,2,3,5,6,…) with appropriate feedback intensity and thresholds. It is argued that this scheme could explain the mechanism of what is called phase compression. Then the phase compression scheme is used to control a spiral wave and spatiotemporal chaos in a network of Chua circuits with 256×256 sites. The numerical simulation results confirm its effectiveness when appropriate upper and bottom thresholds are used by monitoring the measurable output voltages of the chaotic circuit in one site of the network.

Chaos control, spiral wave formation, and the emergence of spatiotemporal chaos in networked Chua circuits

Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this letter we present a feedback scheme to eliminate them. We first collect feedback signals at a certain time t0. Then wait for the system at the excitable position to enter the recovering state. When the time comes, the feedback signals are added. This scheme has two advantages. Firstly, the tip can be eliminated together with the body of spiral wave. Secondly, the injected feedback signals can be very weak and the duration can be very short so that the original system is nearly not to be affected, which is important for practical applications.

Eliminating spiral waves and spatiotemporal chaos using feedback signal

We numerically study trajectories of spiral-wave cores in excitable systems modulated proportionally to the integral of the activity on a straight line, several or dozens of equi-spaced measuring points on a straight line, a double line and a contour line. We show the single-line feedback results in the drift of core center along a straight line being parallel to the detector. An interesting finding is that the drift location in y is a piecewise linear increasing function of both the feedback line location and time delay. A similar trajectory occurs when replacing the feedback line with several or dozens of equi-spaced measuring points on the straight line. This allows to move the spiral core to the desired location along a chosen direction by measuring several or dozens of points. Under the double-line feedback, the shape of the tip trajectory representing the competition between the first and second feedback lines is determined by the distance of two lines. Various drift attractors in spiral wave controlled by square-shaped contour line feedback are also investigated. A brief explanation is presented.

Control of spiral-wave dynamics using feedback signals from line detectors

We study the effects of a dichotomous periodic force on meandering and rigidly rotating spiral waves. For a meandering state, the periodic forcing induces more modulating frequencies according to the rules of frequency-locked relations and linear combinations. It can also generate some unique closed tip orbits. On the modulating period T-axis, there exist all kinds of resonant entrainment bands. Arnold tongues exist in the period-amplitude space. The width of entrainment bands is affected by the symmetry of positive and negative parts in each signal unit. In addition, appropriate choices of T-value can be used to eliminate spiral waves. For a rigidly rotating state, the periodic forcing can induce a transition toward meandering spiral waves via generating a transitive bidirectional spiral wave. It is very interesting that, after the transition, the meandering spiral wave has the same primary rotating period as the free meandering states.

Dynamics of spiral waves driven by a dichotomous periodic signal

Spiral dynamics in the complex Ginzburg–Landau equation (CGLE) with a feedback control are studied. It is shown that the spiral tip follows a circular pathway centered at the measuring point after some transients. The attractor radius is a piecewise constant function of the initial distance between the spiral tip and the measuring point, and a piecewise linear increasing function of the time delay in the feedback loop. Many bumps or lobes can be formed from the circular attractor if the time delay becomes relatively long, and the tip path becomes complex. With an increase in the positive feedback gain, the attractor is not changed, but the drift velocity of the spiral tip along such an attractor is linearly increased. When the gain is negative, the tip is attracted to the measuring point from its initial position if the initial distance is relatively small. The variation of the scaling parameter $$\mu $$
 in CGLE initiates also transitions between attractors of different size, and the attractor radius is a piecewise function of $$\mu $$
 , where it is inversely proportional to a square root of the parameter on each piece. It is also demonstrated that the tip drift velocity has a power-law relation with $$\mu $$
 and the wave speed. Some results can be understood by analyzing the drift direction of the spiral tip in the transient process.

Feedback-controlled dynamics of spiral waves in the complex Ginzburg–Landau equation

The attracting and repelling of spiral waves in a two-dimensional excitable medium in the presence of localized excitability inhomogeneities are studied. The choice of two effects depends on the comparison of excitabilities inside and outside the localized obstacle. We inspect the changes in attracting and repelling behaviors with respect to the size of the obstacle and the initial distance between the center of the spiral core and the obstacle. To understand the occurrence of these phenomena, we investigated the small $v$-value areas near the tip and the function of the wave velocity as the excitability parameter $\ensuremath{\varepsilon}$. Considering the attributes of the attractive obstacle, an eliminating scheme of spiral waves is proposed in which the attractive obstacle is rapidly moved at several fixed times. This method can avoid the high-amplitude and high-frequency stimulus in most conventional methods.

Guoyong Yuan

Papers

Eliminating spiral waves and spatiotemporal chaos using feedback signal

Control of spiral-wave dynamics using feedback signals from line detectors

Dynamics of spiral waves driven by a dichotomous periodic signal

Feedback-controlled dynamics of spiral waves in the complex Ginzburg–Landau equation

Attractive and repulsive contributions of localized excitability inhomogeneities and elimination of spiral waves in excitable media