Multi-periodic States Research Articles

Multiperiodic states and bifurcations in bunch lengthening by a localized impedance in electron storage ring

The equilibrium particle distribution of a bunch in an electron storage ring is investigated using a localized constant wake function. It is shown that, under some conditions, stable multiperiodic states can exist simultaneously. When moving around the parameter space, the system can show bifurcation phenomena which is not always reversible. We study this behavior using the Gaussian approximation and compare the results with multiparticle tracking. The results show qualitative agreement.

Self-evolution neural model

We discuss a self-evolution neural network. The network is usually in the quiescent chaotic state. When a stimulus is applied, the network jumps into the active thinking state and can recognize the input clearly for a time. As time goes on, the network falls into the multiperiodic state gradually and automatically. At last the network slips into the quiescent chaotic state. The self-evolution behavior of the brain can be simply simulated with this model.

Regular and Chaotic Spatiotemporal Patterns in a Model of Slime Mold Aggregation11The project supported by National Natural Science Foundation of China

In this paper we proposed a spatial modulated two-variable Martiel–Goldbeter model to describe the complex spatiotemporal disorder dynamical behavior during development of Dictyostelium discoideum strain FR17. As the nonlinear modulated parameter A and diffusion coefficient varied, the system shows: 1) multiperiodic phase, 2) co-existence phase of chaotic and multi-periodic state, 3) spatiotemporal chaotic phase, 4) co-existence phase of chaotic, multi-periodic and steady state, and 5) co-existence phase of chaotic and steady state. These phases can be described by spatiotemporal power spectra, pattern distribution function and Lyapunov spectra. We believed that the complex spatiotemporal disorder dynamical behavior during development of Dictyostelium discoideum strain FR17 is a spatiotemporal chaotic state.

Market Equilibrium in a Multiperiod State Preference Model with Logarithmic Utility

Market Equilibrium in a Multiperiod State Preference Model with Logarithmic Utility