Transition Of Spiral Wave Research Articles

Impact of Bounded Noise and Rewiring on the Formation and Instability of Spiral Waves in a Small-World Network of Hodgkin-Huxley Neurons.

Spiral waves are observed in the chemical, physical and biological systems, and the emergence of spiral waves in cardiac tissue is linked to some diseases such as heart ventricular fibrillation and epilepsy; thus it has importance in theoretical studies and potential medical applications. Noise is inevitable in neuronal systems and can change the electrical activities of neuron in different ways. Many previous theoretical studies about the impacts of noise on spiral waves focus an unbounded Gaussian noise and even colored noise. In this paper, the impacts of bounded noise and rewiring of network on the formation and instability of spiral waves are discussed in small-world (SW) network of Hodgkin-Huxley (HH) neurons through numerical simulations, and possible statistical analysis will be carried out. Firstly, we present SW network of HH neurons subjected to bounded noise. Then, it is numerically demonstrated that bounded noise with proper intensity σ, amplitude A, or frequency f can facilitate the formation of spiral waves when rewiring probability p is below certain thresholds. In other words, bounded noise-induced resonant behavior can occur in the SW network of neurons. In addition, rewiring probability p always impairs spiral waves, while spiral waves are confirmed to be robust for small p, thus shortcut-induced phase transition of spiral wave with the increase of p is induced. Furthermore, statistical factors of synchronization are calculated to discern the phase transition of spatial pattern, and it is confirmed that larger factor of synchronization is approached with increasing of rewiring probability p, and the stability of spiral wave is destroyed.

SELECTION OF SPIRAL WAVE IN THE COUPLED NETWORK UNDER GAUSSIAN COLORED NOISE

The selection and breakup of spiral wave in a coupled network is investigated by imposing Gaussian colored noise on the network, respectively. The dynamics of each node of the network is described by a simplified Chua circuit, and nodes are uniformly placed in a two-dimensional array with nearest-neighbor connection type. The transition of spiral wave is detected by changing the coupling intensity, intensity and correlation time τ in the noise. A statistical variable is used to discern the parameter region for breakup of spiral wave and robustness to external noise. Spiral waves emerge in the network when the network with structure of complex-periodic and chaotic properties. It is found that asymmetric coupling can induce deformation of spiral wave, stronger intensity or smaller correlation time in noise does cause breakup of the spiral wave.

Parameter Diversity Induced Multiple Spatial Coherence Resonances and Spiral Waves in Neuronal Network with and Without Noise

Diversity in the neurons and noise are inevitable in the real neuronal network. In this paper, parameter diversity induced spiral waves and multiple spatial coherence resonances in a two-dimensional neuronal network without or with noise are simulated. The relationship between the multiple resonances and the multiple transitions between patterns of spiral waves are identified. The coherence degrees induced by the diversity are suppressed when noise is introduced and noise density is increased. The results suggest that natural nervous system might profit from both parameter diversity and noise, provided a possible approach to control formation and transition of spiral wave by the cooperation between the diversity and noise.

Transition from spiral wave to target wave and other coherent structures in the networks of Hodgkin–Huxley neurons

Transition of spiral wave in the regular networks of Hodgkin–Huxley (H–H) neurons is simulated and discussed in detail when the effect of membrane temperature and forcing current is considered. Neurons are distributed in the sites of two-dimensional array, neurons are connected with complete nearest-neighbor connections, no-flux boundary conditions, appropriate initial values and physiological parameters are used to develop a stable rotating spiral wave. A statistic factor of synchronization is defined to discuss the transition and development of spiral wave in the two parameters space (membrane temperature T and forcing current I), and it is found that spiral wave keeps alive due to positive current forcing and the spiral wave can be removed completely when the temperature is increased to a threshold about T = 22.3 °C at a fixed current intensity. Periodical forcing current is imposed on the networks of neurons globally and locally, respectively. It is found that spiral wave could be suppressed by the new generated traveling wave or target wave when periodical forcing current is imposed on the border of networks of neurons, and the most effective frequency of the external forcing current is close to the intrinsic frequency of the spiral wave of the networks.

DYNAMICS OF SPIRAL WAVE IN THE COUPLED HODGKIN–HUXLEY NEURONS

In this paper, the dynamics of the coupled Hodgkin–Huxley neurons (HHn) is investigated. At first, appropriate initial values and reasonable parameters are used to induce spiral wave in the coupled HHn. The temperature and channel noise are also considered to induce the birth and transition of spiral wave, respectively. It is found that the spiral wave can be generated in the absence of channel noise, and the seed of spiral wave cannot grow up when the intensity of channel noise exceeds the threshold (the noise is distributed on all the channels and s describes the membrane patch, the threshold is suggested with s = 3.2). The spiral wave disappears and all the coupled HHn become homogeneous when the temperature exceeds the threshold about T = 22° C .

Spiral Wave in Small-World Networks of Hodgkin–Huxley Neurons

The effect of small-world connection and noise on the formation and transition of spiral wave in the networks of Hodgkin–Huxley neurons are investigated in detail. Some interesting results are found in our numerical studies. i) The quiescent neurons are activated to propagate electric signal to others by generating and developing spiral wave from spiral seed in small area. ii) A statistical factor is defined to describe the collective properties and phase transition induced by the topology of networks and noise. iii) Stable rotating spiral wave can be generated and keeps robust when the rewiring probability is below certain threshold, otherwise, spiral wave can not be developed from the spiral seed and spiral wave breakup occurs for a stable rotating spiral wave. iv) Gaussian white noise is introduced on the membrane of neurons to study the noise-induced phase transition on spiral wave in small-world networks of neurons. It is confirmed that Gaussian white noise plays active role in supporting and developing spiral wave in the networks of neurons, and appearance of smaller factor of synchronization indicates high possibility to induce spiral wave.

Development and transition of spiral wave in the coupled Hindmarsh–Rose neurons in two-dimensional space

The dynamics and the transition of spiral waves in the coupled Hindmarsh–Rose (H–R) neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D′, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons (or sites) and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.