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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. 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


	3. 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


	4. Intrinsic Knots Produced by Large Deformation in 3-Space I: Curvatures
	Xiao Jianhua
	Mechanics 17 October 2007
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	Abstract:For a medium suffered large deformation, knots may be produced internally. Such a kind of knotted medium will reduce the elasticity of the medium. In this research, intrinsic knot production conditions are formulated by the deformation tensor in 3-space. Hence, the traditional continuity concept is replaced with path-connected continuity concept. For a spring produced by deformation, the curvatures of spring are formulated by the intrinsic local rotation angular which is determined by the asymmetrical displacement gradient components. The corresponding deformation energy functionals are formulated, also. They form the basic theoretic formulation of knots for finite deformation mechanics in Chen rational mechanics frame. Finally, the deformation energy of knotted medium is discussed with the knot representation polynomials. These results is expected to be valuable for many practical mechanic engineering problems, such as fatigue-crack, damage/risk evaluation, and elastoplastic instability, especially for understanding and formulating the non-linear dynamics of finite deformation.
	TO cite this article:Xiao Jianhua. Intrinsic Knots Produced by Large Deformation in 3-Space I: Curvatures[OL].[17 October 2007] http://en.paper.edu.cn/en_releasepaper/content/15736

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