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.
In this paper, the evolution of the pattern transition induced by the vortical electric field （VEF） is investigated. Firstly, a scheme is suggested to generate the VEF by changing the spatial magnetic field. Secondly, the VEF is imposed on the whole medium, and the evolutions of the spiral wave and the spatiotemporal chaos are investigated by using the numerical simulation. The result confirms that the drift and the breakup of the spiral wave and the new net-like pattern are observed when different polarized fields are imposed on the whole medium respectively. Finally, the pattern transition induced by the polarized field is discussed theoretically.
This work investigates the effects of the excluded volume and especially those of the chain stiffness on the structural and dynamical properties of a model polymer chain. The theoretical framework is the same as in the recent works by Steinhauser et al., where a Rouse approach is adopted. Our model differs in that our chains have a finite average bending angle. As in the works by Steinhauser et al., Langevin dynamic simulations were performed without hydrodynamic interactions. Whereas this doesn＇t impact the static properties we obtain, it also allows us to compare our results on dynamic properties to those predicted by Rouse theory, where hydrodynamic interactions are also neglected. Our results show that the structural properties are very sensitive to the chain stiffness, whereas the dynamic scaling laws remain the same as those by Rouse theory, with the prefactor depending on the persistence length.
