Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation between two species as another positive feedback is added to a generic interlinked positive-feedback-loop model originating from many realistic biological circuits.A stochastic fluctuation of the positive feedback strength is introduced in a bistable interval of the feedback strength,and bistability appears for the moderate feedback strength at a certain noise level.Stability analysis based on the potential energy landscape is further utilized to explore the noise-induced switching behavior of two stable steady states.
Spiking regularity in a clustered Hodgkin–Huxley(HH) neuronal network has been studied in this letter. A stochastic HH neuronal model with channel blocks has been applied as local neuronal model. Effects of the internal channel noise on the spiking regularity are discussed by changing the membrane patch size. We find that when there is no channel blocks in potassium channels, there exist some intermediate membrane patch sizes at which the spiking regularity could reach to a higher level. Spiking regularity increases with the membrane patch size when sodium channels are not blocked. Namely, depending on different channel blocking states, internal channel noise tuned by membrane patch size could have different influence on the spiking regularity of neuronal networks.
Chua's circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua's circuit system with the smooth degree of 3 are studied. The parametric areas of stability are specified in detail. It is found that the bifurcation graphs of the supercritical and irregular pitchfork bifurcations are similar to those of the piecewise-smooth continuous(PWSC) systems caused by piecewise smoothness. However, the bifurcation graph of the supercritical Hopf bifurcation is similar to those of smooth systems. Therefore, the boundary equilibrium bifurcations of the non-smooth systems with the smooth degree of 3 should receive more attention due to their special features.
