Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux [PDF]
, 2016 State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time.
Balasuriya, Sanjeeva
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Eventual stability and eventual boundedness for impulsive differential equations with “supremum”
Mathematical Modelling and Analysis, 2011 Eventual stability and eventual boundedness for nonlinear impulsive differential equations with supremums are studied. The impulses take place at fixed moments of time. Piecewise continuous Lyapunov functions have been applied.
Ivanka Stamova
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On the existence of periodic solution of some quasilinear differential equations with impulses
Vietnam Journal of Mechanics, 2004 As for ordinary differential equations, one of the problems that especially attract the attention of many mathematicians is the problem on the existence of periodic solutions of the differential equation systems with impulses.
Le Luong Tai
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Multiple Periodic Solutions and Fractal Attractors of Differential Equations with n-Valued Impulses
Mathematics, 2020 Ordinary differential equations with n-valued impulses are examined via the associated Poincaré translation operators from three perspectives: (i) the lower estimate of the number of periodic solutions on the compact subsets of Euclidean spaces and, in ...
Jan Andres
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Oscillations of Second-Order Nonlinear Ordinary Differential Equations with Impulses
Journal of Mathematical Analysis and Applications, 1999 Here, the second-order nonlinear differential equation with impulses of the form \[ \begin{aligned} &[r(t)x'(t)]'+f(t,x(t))=0,\quad t\geq t_0,\;t\neq t_k,\;k=1,2,\dots ,\\ &x(t_k^{+})=g_k(x(t_k)),\;x'(t_k^{+})=h_k(x'(t_k)),\;\;k=1,2,\dots ,\\ &x(t_0^{+})=x_0,\;\;x'(t_0^{+})=x'_0, \end{aligned} \] with \(0\leq ...
Luo, Jiaowan, Debnath, Lokenath
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Asymptotic construction of pulses in the Hodgkin Huxley model for myelinated nerves [PDF]
, 2005 A quantitative description of pulses and wave trains in the spatially discrete Hodgkin-Huxley model for myelinated nerves is given. Predictions of the shape and speed of the waves and the thresholds for propagation failure are obtained.
Carpio, A.
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Some applications of Laplace transforms in models with impulses or discontinuous forcing functions [PDF]
Revista Brasileira de Ensino de FísicaCommonly, in Ordinary Differential Equations courses, equations with impulses or discontinuous forcing functions are studied. In this context, the Laplace Transform of the Dirac delta function and unit step function is taught, which are used as forcing ...
Diego Miranda Gonçalves +1 more
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Numerical calculations near spatial infinity [PDF]
, 2006 After describing in short some problems and methods regarding the smoothness of null infinity for isolated systems, I present numerical calculations in which both spatial and null infinity can be studied.
Zenginoglu, Anil
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Bulletin des Sciences Mathématiques, 2013 Abstract We consider a class of functional differential equations with variable impulses and we establish new stability results. We discuss the variational stability and variational asymptotic stability of the zero solution of a class of generalized ordinary differential equations where our impulsive functional differential equations can be embedded ...
Afonso, S.M. +3 more
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Periodic solutions for ordinary differential equations with sublinear impulsive effects
Journal of Mathematical Analysis and Applications, 2005 The authors investigate the existence of periodic solutions for ordinary differential equations with sublinear impulsive effects.
Qian, Dingbian, Li, Xinyu
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