Introduction to Functional Differential Equations

By Shangjiang Guo, Jianhong Wu. 2013

2,101 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2890800f80c3c6bc98f37995e6a49aeac948c636

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In Computational Theory and Mathematics

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Citations in the corpus

Leaderless and Leader-Following Consensus With Communication and Input Delays Under a Directed Network Topology (2011, methodology): “Proof: Similar to the analysis given in Section IV-C, by using the Leibniz–Newton formula [19], we transform (23) to the following system:”
Stability and Boundary Stabilization of 1-D Hyperbolic Systems (2016, background): “Hale and Verduyn-Lunel (2002) and Michiels and Vyhlidal (2005) ).”
Output feedback control for a class of stochastic high‐order nonlinear systems with time‐varying delays (2014, methodology): “The Lyapunov– Krasovskii method and Lyapunov–Razumikhin method are two powerful tools in the stability analysis and robust control problem for time-delay systems [14].”
Stability of general virus dynamics models with both cellular and viral infections and delays (2017, background): “We note that the system ((4)–(6)) with initial conditions (7) has a unique solution [48].”
Multiplicity-induced-dominancy for delay-differential equations of retarded type (2020, background): “We refer to [3, 18, 19, 25, 32, 34] for more details on time-delay systems and their applications.”
A spectral element approach for the stability of delay systems (2011, background): “However, although the inclusion of delays often leads to more realistic models, the resulting infinite-dimensional state– space significantly complicates the analysis [11, 12].”
On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities (2014, neutral): “See [26,10,6,28] for more details.”
Razumikhin‐type theorems on general decay stability and robustness for stochastic functional differential equations (2012, neutral): “Hale JK, Meyer KR.”
Delay‐dependent robust H∞ controller synthesis for discrete singular delay systems (2011, background): “Singular systems, also called descriptor systems, semistate-space systems and generalized statespace systems, frequently appear in various engineering systems, such as aircraft attitude control systems, flexible robots, large-scale electric networks, chemical engineering systems and lossless transmi”
Joint Communication and Control for Wireless Autonomous Vehicular Platoon Systems (2018, methodology): “Based on the Lyapunov-Razumikhin theorem introduced in [41], if V̇ (e) ≤ 0, i.”
A delayed SIR epidemic model with a general incidence rate (2013, background): “By the fundamental theory of functional differential equations [15], it is easy to show that there exists a unique solution (S(t), I(t)) of system (1.”
Stabilization of Delay Systems: Delay-Dependent Impulsive Control (2017, background): “INTRODUCTION DELAY systems have been extensively studied in last decades due to their widely applications in many fields such as neural networks [1], [2], biology [3], manufacturing processes [4] and information technology [5], [6], and there are significant contributions in the literatures, see [7]”
Formulation of the normal form of Turing-Hopf bifurcation in partial functional differential equations (2020, methodology): “By [25], the phase space C is decomposed by i : C = Pi ⊕ Qi, where Qi = {φ ∈ C : (ψ, φ)ki = 0, for all ψ ∈ P ∗ i }, and P ∗ i , associated with i , is the generalized eigenspace of the formal adjoint differential equation of Eq.”
Stability and global Hopf bifurcation in toxic phytoplankton–zooplankton model with delay and selective harvesting (2013, methodology): “System (4) admits uniqueness and positivity of the solutions by the fundamental theory in [19].”