International Journal of Non-Linear Mechanics, 2011
In the study of dynamical systems, the spectrum of Lyapunov exponents has been shown to be an eff... more In the study of dynamical systems, the spectrum of Lyapunov exponents has been shown to be an efficient tool for analyzing periodic motions and chaos. So far, different calculating methods of Lyapunov exponents have been proposed. Recently, a new method using local mappings was given to compute the Lyapunov exponents in non-smooth dynamical systems. By the help of this method
Based on the inequality analysis, matrix theory and spectral theory, a class of general periodic ... more Based on the inequality analysis, matrix theory and spectral theory, a class of general periodic neural networks with delays and impulses is studied. Some sufficient conditions are established for the existence and globally exponential stability of a unique periodic solution. Furthermore, the results are applied to some typical impulsive neural network systems as special cases, with a real-life example to show feasibility of our results.
Integer multiple spiking due to Gaussian white noise (GWN) occurs near a subcritical Hopf bifurca... more Integer multiple spiking due to Gaussian white noise (GWN) occurs near a subcritical Hopf bifurcation of the Chay system. According to the bistability of dynamics "before" subcritical Hopf bifurcation and the response of the system near the Hopf bifurcation to weak pulses based on the characteristic of GWN, the deterministic Chay system supplied with certain weak pulses can fire integer
Various interspike intervals (ISIs) in a series of spontaneous discharges of experimental neural ... more Various interspike intervals (ISIs) in a series of spontaneous discharges of experimental neural pacemakers were identified as chaotic and as lying between stable period 2 and stable period 3. The method of So et al. for detection of unstable periodic orbits (UPOs) was applied to analyze two chaotic ISI series generated under the action of [Ca2+]o in different concentrations. In the chaotic ISI series near the stable period 2, an unstable period 2 orbit was detected. In the chaotic ISI series near the stable period 3, both an unstable period 2 orbit and an unstable period 3 orbit were detected. The location of the unstable period 2 orbit was close to that of the stable period 2 in the return map, while the location of the unstable period 3 orbit was close to that of the stable period 3. The results not only revealed the structures of various chaotic ISI series, but also indicated that the classification of UPOs could reflect the experimental control parameters at which the chaotic ISI series were generated. The previously discovered period adding bifurcation in the ISI series generated by experimental neural pacemakers [12] was further described in terms of the evolution of the period orbits.
An obvious defect in the DiFrancesco-Noble (DN) model was found, so methods to overcome this inad... more An obvious defect in the DiFrancesco-Noble (DN) model was found, so methods to overcome this inadequacy are put forward. Based on these methods, different kinds of modified DN model can be obtained, and numerical results show that most of the dynamics of the DN model can be essentially preserved by these modified systems.
Communications in Nonlinear Science and Numerical Simulation, 2008
Bursting is an important electrical behavior in neuron’s firing. In this paper, based on the fast... more Bursting is an important electrical behavior in neuron’s firing. In this paper, based on the fast/slow dynamical bifurcation analysis and the phase plane analysis, two types of bursting are presented in the modified Morris–Lecar neuronal model, and the associated bifurcation mechanisms of switching between the active phase and the silent phase are analyzed. For two coupled bursters, it is found
International Journal of Non-Linear Mechanics, 2011
In the study of dynamical systems, the spectrum of Lyapunov exponents has been shown to be an eff... more In the study of dynamical systems, the spectrum of Lyapunov exponents has been shown to be an efficient tool for analyzing periodic motions and chaos. So far, different calculating methods of Lyapunov exponents have been proposed. Recently, a new method using local mappings was given to compute the Lyapunov exponents in non-smooth dynamical systems. By the help of this method
Based on the inequality analysis, matrix theory and spectral theory, a class of general periodic ... more Based on the inequality analysis, matrix theory and spectral theory, a class of general periodic neural networks with delays and impulses is studied. Some sufficient conditions are established for the existence and globally exponential stability of a unique periodic solution. Furthermore, the results are applied to some typical impulsive neural network systems as special cases, with a real-life example to show feasibility of our results.
Integer multiple spiking due to Gaussian white noise (GWN) occurs near a subcritical Hopf bifurca... more Integer multiple spiking due to Gaussian white noise (GWN) occurs near a subcritical Hopf bifurcation of the Chay system. According to the bistability of dynamics "before" subcritical Hopf bifurcation and the response of the system near the Hopf bifurcation to weak pulses based on the characteristic of GWN, the deterministic Chay system supplied with certain weak pulses can fire integer
Various interspike intervals (ISIs) in a series of spontaneous discharges of experimental neural ... more Various interspike intervals (ISIs) in a series of spontaneous discharges of experimental neural pacemakers were identified as chaotic and as lying between stable period 2 and stable period 3. The method of So et al. for detection of unstable periodic orbits (UPOs) was applied to analyze two chaotic ISI series generated under the action of [Ca2+]o in different concentrations. In the chaotic ISI series near the stable period 2, an unstable period 2 orbit was detected. In the chaotic ISI series near the stable period 3, both an unstable period 2 orbit and an unstable period 3 orbit were detected. The location of the unstable period 2 orbit was close to that of the stable period 2 in the return map, while the location of the unstable period 3 orbit was close to that of the stable period 3. The results not only revealed the structures of various chaotic ISI series, but also indicated that the classification of UPOs could reflect the experimental control parameters at which the chaotic ISI series were generated. The previously discovered period adding bifurcation in the ISI series generated by experimental neural pacemakers [12] was further described in terms of the evolution of the period orbits.
An obvious defect in the DiFrancesco-Noble (DN) model was found, so methods to overcome this inad... more An obvious defect in the DiFrancesco-Noble (DN) model was found, so methods to overcome this inadequacy are put forward. Based on these methods, different kinds of modified DN model can be obtained, and numerical results show that most of the dynamics of the DN model can be essentially preserved by these modified systems.
Communications in Nonlinear Science and Numerical Simulation, 2008
Bursting is an important electrical behavior in neuron’s firing. In this paper, based on the fast... more Bursting is an important electrical behavior in neuron’s firing. In this paper, based on the fast/slow dynamical bifurcation analysis and the phase plane analysis, two types of bursting are presented in the modified Morris–Lecar neuronal model, and the associated bifurcation mechanisms of switching between the active phase and the silent phase are analyzed. For two coupled bursters, it is found
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