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1. Interaction Function of Coupled Bursting Neurons | |||
ZHANG Jiadong, SHI Xia | |||
Mechanics 18 December 2015 | |||
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Abstract:The interaction functions of electrically coupled Hindmarsh-Rose (HR) neurons for different firing patterns are investigated in this paper. By applying the phase reduction technique, the burst phase response curve (BPRC) of the bursting neuron is derived. Then the interaction function of two coupled neurons can be calculated numerically according to the BPRC and the voltage time course of the neuron. Results show that the BPRC is more and more complicated with the increase of the spiking number within a burst, and the curve of the interaction function oscillates more and more frequently with it. However, two certain things are unchanged: $phi=0$, which corresponds to the in-phase synchronization state, is always the stable equilibrium, while the anti-phase synchronization state with $phi=0.5$ is an unstable equilibrium. | |||
TO cite this article:ZHANG Jiadong, SHI Xia. Interaction Function of Coupled Bursting Neurons[OL].[18 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4672312 |
2. Synchronization of a Neuronal Network Consisting of Mixed Bursting Neurons with Hybrid Synapses | |||
XI Wenqi, SHI Xia | |||
Mechanics 18 December 2015 | |||
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Abstract:In this paper, burst synchronization of a small-world neuronal network consisting of mixed bursting types of neurons coupled via inhibitory-excitatory chemical synapses is explored. The quantities, the synchronization parameter, is used to characterize the synchronization degree of the neuronal network. Numerical results show that the percentage of the inhibitory synapses in the network is the major factor for we get a similarly bell-shaped dependence of synchronization on it. We also find that not only the value of the coupling strength can promote the synchronization degree, but also the probability of random edges adding to the small-world network can. The ratio of the long bursting neurons has little effect on the burst synchronization of the network. | |||
TO cite this article:XI Wenqi, SHI Xia. Synchronization of a Neuronal Network Consisting of Mixed Bursting Neurons with Hybrid Synapses[OL].[18 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4672309 |
3. Solitonic shape restoring and soliton complex fora variant Boussinesq system with variable coefficients in fluiddynamics | |||
Wang Lei | |||
Mechanics 29 September 2013 | |||
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Abstract:For the nonlinear and dispersive long gravity waves traveling in twohorizontal directions with varying depth of the water, we consider avariant Boussinesq with variable coefficients (vcvB) system withsymbolic computation. Using the Darboux transformationof the vcAKNS system, we present the double Wronskian-type solutionfor the vcvB system. Two sorts of inelastic interactions for thevcvB system are graphically discussed. | |||
TO cite this article:Wang Lei. Solitonic shape restoring and soliton complex fora variant Boussinesq system with variable coefficients in fluiddynamics[OL].[29 September 2013] http://en.paper.edu.cn/en_releasepaper/content/4561906 |
4. A modified Mickens iteration method for self-excited systems with nonlinear damping terms | |||
Y.M. Chen,J.K. Liu | |||
Mechanics 31 January 2013 | |||
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Abstract:The Mickens iteration method is modified for solving limit cycle oscillations (LCOs) of self-excited systems. Different from other existing procedures, the unknown frequency that arises in the nonlinearity is replaced by the previous iteration value. Therefore, the unknown frequency appears just in linear terms and its square can be considered as an independent parameter. Simpler algebraic equations are then deduced and solved numerically. Numerical examples show the modified algorithm can provide very accurate LC solutions. Since the unknown frequency is uncoupled from nonlinear terms, this approach is rather appropriate for a type of systems with nonlinear damping terms. | |||
TO cite this article:Y.M. Chen,J.K. Liu. A modified Mickens iteration method for self-excited systems with nonlinear damping terms[OL].[31 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4518353 |
5. Algorithm Robustness Analysis for the Choice of Optimal Time Delay of Phase Space Reconstruction Based on Singular Entropy Method | |||
Yao Baoheng | |||
Mechanics 12 January 2011 | |||
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Abstract:The method of Delays is commonly used in state space reconstruction of chaotic time series, and the quality of attractor reconstruction of phase space is sensitive to the choice of embedding parameters, i.e. embedding dimension and time delay. In this paper, a new information measure based on singular entropy (SE) is proposed to choose the optimal time delay in reconstructed dynamical system, which differs from the correlation function method by using singular value fraction (SVF). The robustness of singular entropy algorithm is further discussed, and it shows the advantage of the proposed method. | |||
TO cite this article:Yao Baoheng. Algorithm Robustness Analysis for the Choice of Optimal Time Delay of Phase Space Reconstruction Based on Singular Entropy Method[OL].[12 January 2011] http://en.paper.edu.cn/en_releasepaper/content/4406322 |
6. The N-soliton-like solution and Bäcklund transformation for a non-isospectral and variable-coefficient modified Korteweg-de Vries equation | |||
Qian Feng,Xiang-Hua Meng,Xin Yu,Zhi-Yuan Sun,Tao Xu,Bo Tian,Yi-Tian Gao | |||
Mechanics 06 May 2008 | |||
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Abstract:As an important model mathematically and physically, a non-isospectral and variable-coefficient modified Korteweg-de Vries (mKdV) equation is investigated in this paper. Starting from the Lax pair presented, the Bäcklund transformation in original variables is explicitly deduced. And then, by a dependent variable transformation, the non-isospectral and variable-coefficient mKdV equation is transformed into bilinear equations, by virtue of which the N-soliton-like solution is obtained. Subsequently, through the bilinear Bäcklund transformation gained, the one-soliton-like solution is derived from a vacuum one. Furthermore, the N-soliton-like solution in the Wronskian form is constructed and verified via the Wronskian technique. | |||
TO cite this article:Qian Feng,Xiang-Hua Meng,Xin Yu, et al. The N-soliton-like solution and Bäcklund transformation for a non-isospectral and variable-coefficient modified Korteweg-de Vries equation[OL].[ 6 May 2008] http://en.paper.edu.cn/en_releasepaper/content/21172 |
7. Intermediate processes, critical phenomena: theory, method, progress of fractional operators and its applications to modern mechanics | |||
Xu Mingyu,Tan Wenchang | |||
Mechanics 27 February 2006 | |||
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Abstract:From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equations) used for describing intermediate processes and critical phenomena in physics and mechanics, and their progress in theory and methods, and applications to modern mechanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made. | |||
TO cite this article:Xu Mingyu,Tan Wenchang. Intermediate processes, critical phenomena: theory, method, progress of fractional operators and its applications to modern mechanics[OL].[27 February 2006] http://en.paper.edu.cn/en_releasepaper/content/5390 |
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