Stabilisation of hybrid stochastic differential equations by delay feedback control [PDF]
, 2008 This paper is concerned with the exponential mean-square stabilisation of hybrid stochastic differential equations (also known as stochastic dierential equations with Markovian switching) by delay feedback controls.
Lam, James +10 more
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Neural Delay Differential Equations
CoRR, 2021 Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been successfully developed for conquering some limitations emergent in application of the original framework.
Qunxi Zhu, Yao Guo 0003, Wei Lin 0003
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Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching [PDF]
, 2008 The main aim of this paper is to discuss the almost surely asymptotic stability of the neutral stochastic differential delay equations (NSDDEs) with Markovian switching.
Yuan, Chenggui +7 more
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Distributed Delay Differential Equation Representations of Cyclic Differential Equations [PDF]
SIAM Journal on Applied Mathematics, 2021 Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is equivalent to an Erlang distributed delay differential equation (DDE).
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Approximate solutions of stochastic differential delay equations with Markovian switching [PDF]
, 2010 Our main aim is to develop the existence theory for the solutions to stochastic differential delay equations with Markovian switching (SDDEwMSs) and to establish the convergence theory for the Euler-Maruyama approximate solutions under the local ...
Li, Xiaoyue, Shen, Yi, Mao, Xuerong
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Almost sure exponential stability of numerical solutions for stochastic delay differential equations [PDF]
, 2010 Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (
Szpruch, Lukasz, Wu, Fuke, Mao, Xuerong
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On nonlinear delay differential equations [PDF]
Transactions of the American Mathematical Society, 1994 We examine qualitative behaviour of delay differential equations of the form \[ y ′
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Asymptotic behaviours of stochastic differential delay equations [PDF]
, 2005 Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper.
Shen, Yi +3 more
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Characterising small solutions in delay differential equations through numerical approximations [PDF]
, 2003 This paper discusses how the existence of small solutions for delay differential equations can be predicted from the behaviour of the spectrum of the finite dimensional approximations.Manchester Centre for Computational ...
Ford, Neville J., Lunel, Sjoerd M. V.
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Global Boundedness for a Delay Differential Equation [PDF]
Transactions of the American Mathematical Society, 1986 The inequality ( ∂ t u − Δ u ) ( t , x ) ≤ u ( t , x ) ( 1 − u ( t − τ , x ) )
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