Time-periodic Coupling Strength Research Articles

Inducement and enhancement of multiple coherence resonances in unidirectionally coupled neural systems: Random and time-periodic coupling strength

The effect of cooperative coupling strength (CCS), i.e., random coupling strength and time-periodic coupling strength, on multiple coherence resonances in unidirectionally coupled neural system has been investigated. Results show that noise, frequency and amplitude play efficient roles for the enhancement of various coherent behaviours. There exist an optimal frequency and an optimal amplitude which make the system to display the best coherent behaviours. Furthermore, the novel coherence biresonance (CBR) induced by frequency of CCS and coherence multiresonances (CMR) induced by amplitude of CCS, are found.

Cooperative effect of random and time-periodic coupling strength on synchronization transitions in one-way coupled neural system: mean field approach.

The cooperative effect of random coupling strength and time-periodic coupling strengh on synchronization transitions in one-way coupled neural system has been investigated by mean field approach. Results show that cooperative coupling strength (CCS) plays an active role for the enhancement of synchronization transitions. There exist an optimal frequency of CCS which makes the system display the best CCS-induced synchronization transitions, a critical frequency of CCS which can not further affect the CCS-induced synchronization transitions, and a critical amplitude of CCS which can not occur the CCS-induced synchronization transitions. Meanwhile, noise intensity plays a negative role for the CCS-induced synchronization transitions. Furthermore, it is found that the novel CCS amplitude-induced synchronization transitions and CCS frequency-induced synchronization transitions are found.

Enhancement of temporal coherence via time-periodic coupling strength in a scale-free network of stochastic Hodgkin–Huxley neurons

We investigate the effects of time-periodic coupling strength on the temporal coherence or firing regularity of a scale-free network consisting of stochastic Hodgkin–Huxley (H–H) neurons. The temporal coherence exhibits a resonance-like behavior depending on the cell size or the channel noise intensity. The best temporal coherence requires an optimal channel noise intensity, and this coherence can be significantly increased by time-periodic coupling strength when its frequency matches the integer multiples of the intrinsic subthreshold oscillation frequency of H–H neuron. Particularly, we find the multiple-coherence resonance depending on frequency of time-periodic coupling strength at the optimal noise intensity. We also obtain a resonance-like dependence of temporal coherence on the amplitude of time-periodic coupling strength. Additionally, we investigate the effects of average degree on the temporal coherence and find that the temporal coherence exhibits a resonance-like behavior with respect to the network average degree, indicating that the best regularity requires an optimal average degree.

Phase Response Synchronization in Neuronal Population with Time-Varying Coupling Strength.

We present the dynamic model of global coupled neuronal population subject to external stimulus by the use of phase sensitivity function. We investigate the effect of time-varying coupling strength on the synchronized phase response of neural population subjected to external harmonic stimulus. For a time-periodic coupling strength, we found that the stimulus with increasing intensity or frequency can reinforce the phase response synchronization in neuronal population of the weakly coupled neural oscillators, and the neuronal population with stronger coupling strength has good adaptability to stimulus. When we consider the dynamics of coupling strength, we found that a strong stimulus can quickly cause the synchronization in the neuronal population, the degree of synchronization grows with the increasing stimulus intensity, and the period of synchronized oscillation induced by external stimulation is related to stimulus frequency.

Meandering Spiral Waves Induced by Time-Periodic Coupling Strength

Effects of time-periodic coupling strength (TPCS) on spiral waves dynamics are studied by numerical computations and mathematical analyses. We find that meandering or drifting spirals waves, which are not observed for the case of constant coupling strength, can be induced by TPCS. In particular, a transition between outward petal and inward petal meandering spirals is observed when the period of TPCS is varied. These two types of meandering spirals are separated by a drifting spiral, which can be induced by TPCS when the period of TPCS is very close to that of rigidly rotating spiral. Similar results can be obtained if the coupling strength is modulated by a rectangle wave. Furthermore, a kinetic model for spiral movement suggested by Di et al., [Phys. Rev. E 85 (2012) 046216] is applied for explaining the above findings. The theoretical results are in good qualitative agreement with numerical simulations.

Periodic coupling strength-dependent multiple coherence resonance by time delay in Newman–Watts neuronal networks

Recently, multiple coherence resonance induced by time delay has been observed in neuronal networks with constant coupling strength. In this paper, by employing Newman–Watts Hodgkin–Huxley neuron networks with time-periodic coupling strength, we study how the temporal coherence of spiking behavior and coherence resonance by time delay change when the frequency of periodic coupling strength is varied. It is found that delay induced coherence resonance is dependent on periodic coupling strength and increases when the frequency of periodic coupling strength increases. Periodic coupling strength can also induce multiple coherence resonance, and the coherence resonance occurs when the frequency of periodic coupling strength is approximately multiple of the spiking frequency. These results show that for periodic coupling strength time delay can more frequently optimize the temporal coherence of spiking activity, and periodic coupling strength can repetitively optimize the temporal coherence of spiking activity as well. Frequency locking may be the mechanism for multiple coherence resonance induced by periodic coupling strength. These findings imply that periodic coupling strength is more efficient for enhancing the temporal coherence of spiking activity of neuronal networks, and thus it could play a more important role in improving the time precision of information processing and transmission in neural networks.

Multiple synchronization transitions due to periodic coupling strength in delayed Newman–Watts networks of chaotic bursting neurons

In this paper, we numerically study the effect of time-periodic coupling strength on the synchronization of firing activity in delayed Newman–Watts networks of chaotic bursting neurons. We first examine how the firing synchronization transitions induced by time delay under fixed coupling strength changes in the presence of time-periodic coupling strength, and then focus on how time-periodic coupling strength induces synchronization transitions in the networks. It is found that time delay can induce more synchronization transitions in the presence of time-periodic coupling strength compared to fixed coupling strength. As the frequency of time-periodic coupling strength is varied, the firing exhibits multiple synchronization transitions between spiking antiphase synchronization and in-phase synchronization of various firing behaviors including bursting, spiking, and both bursting and spiking, depending on the values of time delay. These results show that time-periodic coupling strength can increase the synchronization transitions by time delay and can induce multiple synchronization transitions of various firing behaviors in the neuronal networks. This means that time-periodic coupling strength plays an important role in the information processing and transmission in neural systems.

PERIODIC COUPLING STRENGTH-ENHANCED COHERENCE RESONANCE INDUCED BY A PARTICULAR KIND OF NON-GAUSSIAN NOISE IN NEURONAL NETWORKS

In this Letter, we study the effect of time-periodic coupling strength (TPCS) on the coherence resonance (CR) of spiking behavior induced by a particular kind of non-Gaussian noise in Newman–Watts networks of Hodgkin–Huxley neurons. It is found that the CR by the non-Gaussian noise can be enhanced by TPCS when TPCS frequency is equal to or multiple of the inverse of the refractory period, and can occur in networks with more random shortcuts for TPCS than for constant coupling strength. Furthermore, the CR by the non-Gaussian noise can occur at smaller TPCS frequency when network randomness increases. These results show that the CR by the non-Gaussian noise can be enhanced by TPCS and can occur in more complex networks in case of TPCS. These findings may help to better understand the joint roles of the non-Gaussian noise and TPCS in the spiking activity of the neuronal networks.

Dependence of delay-induced coherence resonance on time-periodic coupling strength in Newman-Watts neuronal networks

Recently, delay-induced coherence resonance (CR) in neuronal networks with fixed coupling strength has received much attention. In this paper, we study delay-induced CR in Newman-Watts neuronal networks with time-periodic coupling strength, mainly investigating how CR changes with the varying frequency of time-periodic coupling strength. We find that delay-induced CR become more frequent as the frequency is increased. When the frequency exceeds a threshold value, time delay can induce multiple CR more than for constant coupling strength. Furthermore, delay-induced CR occurs more abruptly and becomes more pronounced for time-periodic coupling strength than for constant coupling strength. These results show that delay-induced CR strongly depends on the coupling strength of neurons, and time delay can optimize spiking coherence more frequently and precisely in the presence of time-periodic coupling strength. This implies that time-periodic coupling strength could be more helpful for time delay to enhance and optimize the spiking coherence, and thus it may play a more efficient role in improving the time precision of information processing in neuronal networks.

Multiple coherence resonances by time-periodic coupling strength in scale-free networks of bursting neurons

In this paper, we study the effect of time-periodic coupling strength (TPCS) and network connection degree ⟨k⟩ on the temporal coherence of the chaotic bursting of the scale-free networks of thermo-sensitive neurons. It is found that the chaotic bursting becomes ordered and can exhibit coherence resonance (CR) when TPCS amplitude e0 or the network connection degree ⟨k⟩ is varied. In particular, the neuronal bursting may exhibit multiple CR (MCR) behavior when TPCS frequency ω is varied. It is also found that, as ⟨k⟩ is increased, the value of e0 for the MCR decreases, but the frequency for the MCR almost keeps unchanged. These results show that the chaotic bursting can be tamed and the bursting temporal coherence can be enhanced and even optimized by TPCS and network connection degree. Furthermore, TPCS can repetitively enhance and even optimize the temporal coherence of the neuronal bursting behavior. These findings may help to better understand the roles of TPCS and network connection degree for improving the time precision of the information processing in neuronal networks.

Coherence resonance and bi-resonance by time-periodic coupling strength in Hodgkin-Huxley neuron networks

We study the effect of time-periodic coupling strength on the spiking coherence of Newman-Watts networks of Hodgkin-Huxley (HH) neurons with non-Gaussian noise. It is found that the spiking can exhibit coherence resonance (CR) when the extent of deviation of non-Gaussian noise from Gaussian noise and the amplitude of the coupling strength are varied. In particular, coherence bi-resonance (CBR) is observed when the frequency of the coupling strength is varied, and the CBR is always observed when the frequency is equal to, or a multiple of, the spiking period, manifesting as the locking between the frequencies of the spiking and the coupling strength. The results show that a time-periodic coupling strength may play a more constructive and efficient role in enhancing the spiking coherence of the neuronal networks than a constant coupling strength. These findings provide insight into the role of time-periodic coupling strength for enhancing the time precision of information processing in neuronal networks.

Ordered chaotic bursting and multiple coherence resonance by time-periodic coupling strength in Newman–Watts neuronal networks

In this paper, we study the effect of time-periodic coupling strength (TPCS) on the temporal coherence of the chaotic bursting of Newman–Watts thermosensitive neuron networks. It is found that the chaotic bursting can exhibit coherence resonance and multiple coherence resonance behavior when TPCS amplitude and frequency is varied, respectively. It is also found that TPCS can also enhance the temporal coherence and spatial synchronization of the optimal spatio-temporal bursting in the case of fixed coupling strength. These results show that TPCS can tame the chaotic bursting and can repeatedly enhance the temporal coherence of the chaotic bursting neuronal networks. This implies that TPCS may play a more efficient role for improving the time precision of the information processing in chaotic bursting neurons.

Multiple coherence resonance induced by time-periodic coupling in stochastic Hodgkin–Huxley neuronal networks

In this paper, we study the effect of time-periodic coupling strength (TPCS) on the spiking coherence of Newman-Watts small-world networks of stochastic Hodgkin-Huxley (HH) neurons and investigate the relations between the coupling strength and channel noise when coherence resonance (CR) occurs. It is found that, when the amplitude of TPCS is varied, the spiking induced by channel noise can exhibit CR and coherence bi-resonance (CBR), and the CR moves to a smaller patch area (bigger channel noise) when the amplitude increases; when the frequency of TPCS is varied, the intrinsic spiking can exhibit CBR and multiple CR, and the CR always occurs when the frequency is equal to or multiple of the spiking period, manifesting as the locking between the frequencies of the intrinsic spiking and the coupling strength. These results show that TPCS can greatly enhance and optimize the intrinsic spiking coherence, and favors the spiking with bigger channel noise to exhibit CR. This implies that, compared to constant coupling strength, TPCS may play a more efficient role for improving the time precision of the information processing in stochastic neuronal networks.

Resonance tongues in a system of globally coupled FitzHugh–Nagumo oscillators with time-periodic coupling strength

We investigate the dynamics of a population of globally coupled FitzHugh-Nagumo oscillators with a time-periodic coupling strength. While for synchronizing global coupling, the in-phase state is always stable, the oscillators split into several cluster states for desynchronizing global coupling, most commonly in two, irrespective of the coupling strength. This confines the ability of the system to form n:m locked states considerably. The prevalence of two and four cluster states leads to large 2:1 and 4:1 subharmonic resonance regions, while at low coupling strength for a harmonic 1:1 or a superharmonic 1:m time-periodic coupling coefficient, any resonances are absent and the system exhibits nonresonant phase drifting cluster states. Furthermore, in the unforced, globally coupled system the frequency of the oscillators in a cluster state is in general lower than that of the uncoupled oscillator and strongly depends on the coupling strength. Periodic variation of the coupling strength at twice the natural frequency causes each oscillator to keep oscillating with its autonomous oscillation period.