Burst synchronization of electrically and chemically coupled map-based neurons

Burst synchronization and burst dynamics of a system consisting of two map-based neurons coupled through electrical or chemical synapses are discussed. Some basic characteristic quantities are introduced to describe burst synchronization and burst dynamics of neurons. It is observed that excitatory coupling leads to in-phase burst synchronization but inhibitory coupling results in anti-phase one. By using the basic characteristics of burst dynamics, the effects of the intrinsic bursting properties and the coupling schemes on complex bursting behaviors are also presented for both inhibitory and excitatory couplings. The results are instructive to identify bursting behaviors through experimental data.     

Stability and bifurcation analysis in the coupled HR neurons with delayed synaptic connection

Nonlinear Dynamics - This paper presents stability and bifurcations of two synaptically coupled identical Hindmarsh–Rose neurons with one time delay. The parameters we choose contribute to...     

The effect of diffusion on the permanence of Smith population model in a polluted patch

IntroductionThe effect of diffusion on the permanence of population has been studied in some refer-ences. LevinI1] set up the followiIlg model to study the effect of diffusion on the permanence ofpopulation:: f \' \ =.tvhere ur(t) defines the number of population i in patch p, uu = (ut,'. u:). f,u(uu) isthe int!.i11sic growth rate fOr population t, and D:' is the (1iffosive rate of population l frompatch 7 to patch U. Hastingsi2J proved that the positive equilibrium state is stab1e for suf…     

Impulsive state feedback control of a predator–prey model

The dynamics of a predator–prey model with impulsive state feedback control, which is described by an autonomous system with impulses, is studied. The sufficient conditions of existence and stability of semi-trivial solution and positive period-1 solution are obtained by using the Poincaré map and analogue of the Poincaré criterion. The qualitative analysis shows that the positive period-1 solution bifurcates from the semi-trivial solution through a fold bifurcation. The bifurcation diagrams of periodic solutions are obtained by using the Poincaré map, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations.     

Planar motion and stability for a rigid body with a beam in a field of central gravitational force

Planar motion for a rigid body with an elastic beam in a field of central gravitational force was investigated, and both of the orbital motion and attitude motion were under consideration. The equations of motion of the system were derived by the variational principle, and on view point of generalized Hamiltonian dynamics, the sufficient conditions for the stability of one class of relative equilibria were given by the energymomentum method.     

Exact bounds for the sensitivity analysis of structures with uncertain-but-bounded parameters

Based on interval mathematical theory, the interval analysis method for the sensitivity analysis of the structure is advanced in this paper. The interval analysis method deals with the upper and lower bounds on eigenvalues of structures with uncertain-but-bounded (or interval) parameters. The stiffness matrix and the mass matrix of the structure, whose elements have the initial errors, are unknown except for the fact that they belong to given bounded matrix sets. The set of possible matrices can be described by the interval matrix. In terms of structural parameters, the stiffness matrix and the mass matrix take the non-negative decomposition. By means of interval extension, the generalized interval eigenvalue problem of structures with uncertain-but-bounded parameters can be divided into two generalized eigenvalue problems of a pair of real symmetric matrix pair by the real analysis method. Unlike normal sensitivity analysis method, the interval analysis method obtains informations on the response of structures with structural parameters (or design variables) changing and without any partial differential operation. Low computational effort and wide application rang are the characteristic of the proposed method. Two illustrative numerical examples illustrate the efficiency of the interval analysis.     

High-T c superconducting thin film/GaAs MESFET hybrid microwave oscillator

A high-T _c superconducting (HTSC) thin film/GaAs MESFET hybrid microwave oscillator operated at 10.6 GHz has been designed, fabricated and characterized. Microstrip line structures were used throughout the circuit with superconducting thin film YBa₂Cu₃O_7-δ(YBCO) as the conductor material. The YBCO thin films were deposited on 15 mm×10 mm×0.5 mm LaAlO₃ substrates. The oscillator was common-source, series feedback type using a GaAs-MESFET (NE72084) as the active device and a superconducting microstrip resonator as the frequency stabilizing element. By improving the unloaded quality factorQ ₀ of the superconducting microstrip resonator and adjusting the coupling coefficient between the resonator and the gate of the MESFET, the phase noise of the oscillator was decreased. At 77 K, the phase noise of the oscillator at 10 kHz offset from carrier was −87 dBc/Hz. Project supported by the National Center for Research and Development on Superconductivity of China.     

在激发介质中单扩散回卷波组织中心的运动

应用奇异摄动方法,讨论了在单扩散型激发介质中无扭曲的三维回卷波组织中心的运动规律.确定了无扭曲的组织中心的曲率关系和线性律,这些结果具有明显的物理意义,而且与实验符合得很好.     

Nonlinear normal modes and their superposition in a two degrees of freedom asymmetric system with cubic nonlinearities

This paper investigates nonlinear normal modes and their superposition in a two degrees of freedom asymmetric system with cubic nonlinearities for all nonsingular conditions, based on the invariant subspace in nonlinear normal modes for the nonlinear equations of motion. The focus of attention is to consider relation between the validity of superposition and the static bifurcation of modal dynamics. The numerical results show that the validity has something to do not only with its local restriction, but also with the static bifurcation of modal dynamics. Project Supported by the National Natural Science Foundation and PSF of China     

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities： experiments and analysis

Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast-slow dynamics analysis for classification and mechanism of various bursting patterns, one- or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities （stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.）. Thirdly, different types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.