Ordinary differential equations with impulses

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Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks. [PDF]

Nat Commun
Regazzoni F +4 more
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A novel pulse-modulated closed-loop artificial pancreas based on intravenous administration of insulin and glucagon. [PDF]

Sci Rep
Goede SL +4 more
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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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Galerkin Methods for Nonlinear Ordinary Differential Equation with Impulses

Numerical Algorithms, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
François Dubeau, Abdelatif Ouansafi, A. Sakat +2 more
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Stability of functional differential equations with variable impulsive perturbations via generalized ordinary differential equations

Bulletin Des Sciences Mathematiques, 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 ...
S M Afonso, E M Bonotto, M Federson
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Asymptotic equivalence of ordinary and impulsive operator–differential equations

Communications in Nonlinear Science and Numerical Simulation, 2019
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Anatoliy A. Martynyuk, Gani Tr. Stamov, Ivanka M. Stamova +2 more
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INTEGRAL SURFACES FOR HYPERBOLIC ORDINARY DIFFERENTIAL EQUATIONS WITH IMPULSES

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 1985
The paper considers integral surfaces of systems of differential equations with impulse perturbations at fixed moments of time. Sufficient conditions have been obtained for the existence of integral surfaces with definite properties and the behaviour of the solutions has been studied with initial conditions outside these surfaces.
Hristova, S. G., Bainov, D. D.
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Ordinary dichotomy and perturbations of the impulse matrices of linear impulsive differential equation

International Journal of Theoretical Physics, 1990
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Milev, N. V., Bajnov, D. D.
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Boundary value problems for higher order ordinary differential equations with impulses

Nonlinear Analysis: Theory, Methods & Applications, 1998
The authors use the method of upper and lower solutions coupled with a monotone iterative technique, to study existence and approximation of solutions to some boundary value problems for higher-order ordinary differential equations with impulses of the type \[ u^{(n)}(t) = f(t,u(t)), \text{ for } \;a.e.
Alberto Cabada, Eduardo Liz
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On Impulsive Ordinary and Delay Differential Equations

2002
Existence and uniqueness of the solution to ordinary and delay differential equations with infinitely many state-dependent impulses are considered. A simple transformation allows us to show that these problems are equivalent to problems without impulse. A fixed point approach is then applied for an appropriate norm.
François Dubeau +3 more
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mathematics
impulses