Fusionable and fissionable waves of (2+1)-dimensional shallow water wave equation

We investigate a (2+1)-dimensional shallow water wave equation and describe its nonlinear dynamical behaviors in physics. Based on the N-soliton solutions, the higher-order fissionable and fusionable waves, fissionable or fusionable waves mixed with soliton molecular and breather waves can be obtained by various constraints of special parameters. At the same time, by the long wave limit method, the interaction waves between fissionable or fusionable waves with higher-order lumps are acquired. Combined with the dynamic figures of the waves, the properties of the solution are deeply studied to reveal the physical significance of the waves.     

Noise-induced synchronous stochastic oscillations in small scale cultured heart-cell networks

This paper reports that the synchronous integer multiple oscillations of heart-cell networks or clusters are observed in the biology experiment.The behaviour of the integer multiple rhythm is a transition between super-and subthreshold oscillations,the stochastic mechanism of the transition is identified.The similar synchronized oscillations are theoretically reproduced in the stochastic network composed of heterogeneous cells whose behaviours are chosen as excitable or oscillatory states near a Hopf bifurcation point.The parameter regions of coupling strength and noise density that the complex oscillatory rhythms can be simulated are identified.The results show that the rhythm results from a simple stochastic alternating process between super-and sub-threshold oscillations.Studies on single heart cells forming these clusters reveal excitable or oscillatory state nearby a Hopf bifurcation point underpinning the stochastic alternation.In discussion,the results are related to some abnormal heartbeat rhythms such as the sinus arrest.     

Stochastic Alternating Dynamics for Synchronous EAD-Like Beating Rhythms in Cultured Cardiac Myocytes

Dissolved cardiac myocytes can couple together and generate synchronous beatings in culture. We observed a synchronized early after-depolarization（EAD）-like rhythm in cultured cardiac myocytes and reproduced the experimental observation in a network mathematical model whose dynamics are close to a Hopf bifurcation. The mechanism for this EAD-like rhythm is attributed to noised-induced stochastic alternatings between the focus and the limit cycle. These results provide novel understandings for pathological heart rhythms like the early immature beatings.     

相位噪声诱发神经放电的单次或两次相干共振

神经元电活动可以从静息通过Hopf分岔到放电,放电频率有固定周期;也可以从静息通过鞍-结分岔到放电,放电频率接近零.在具有周期性的相位噪声作用下的Hopf分岔和鞍-结分岔点附近,都会产生相干共振.噪声的周期小于Hopf分岔点附近的放电的周期时,相位噪声可以引起神经系统产生一次相干共振,位于系统内在的固有频率附近;噪声的周期大于系统的固有周期时,相位噪声可以引起双共振,对应低噪声强度的共振产生在噪声频率附近,对应高噪声强度的共振产生在系统的固有频率附近;并对双共振的产生原因进行了解释.在鞍-结分岔点附近,无论噪声的周期是大是小,都只会引起一次共振,研究结果不仅揭示了相位噪声作用下平衡点分岔点相干共振的动力学特性和对应于两类分岔的两类神经兴奋性的差别,还对近期的相位噪声诱发产生单或双共振的不同研究结果给出了解释.     

利用相位响应曲线解释抑制性反馈增强神经电活动

在众多实验和理论研究中已经发现自突触通过自反馈电流调节神经元电活动和网络时空行为来实现生理功能.本文通过理论研究,发现在一些合适的时滞下,抑制性自反馈电流能引起放电频率增加,这是不同于传统结果—抑制性作用引起频率降低的新发现.进一步,对于没有自反馈的神经元,发现在作用相位合适的抑制性脉冲电流的作用下,放电的相位会提前,导致放电频率增加,这就表现出对应Hopf分岔的II型相位响应曲线的特征.引起放电频率增加的抑制性脉冲刺激的相位与自反馈的时滞相对应,这也就给出了自反馈能够引起放电频率增强的原因.最后,发现抑制性自反馈的时滞较长或耦合强度较大时,噪声诱发的神经元放电峰-峰间期的变异系数较小,也就是放电精确性提高,与实验发现的慢抑制性自突触诱发放电精确性增加的结果相一致.研究结果揭示了负反馈能增强系统响应这一新现象和相应的非线性动力学机制,提供了调控神经电活动的新手段,有助于认识现实神经系统的自突触的潜在功能.