Comparison principle and stability of differential equations with piecewise constant arguments

Alwan, Mohamad S.; Liu, Xinzhi; Xie, Wei‐Chau

doi:10.1016/j.jfranklin.2012.08.016

Cited by 16 publications

(3 citation statements)

References 19 publications

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“…Alwan et al [7] developed a comparison principle to establish some stability properties for nonlinear EPCA. In [8], the existence and uniqueness of almost periodic solution of EPCA were considered.…”

Section: Introductionmentioning

confidence: 99%

Stability and Oscillation of Mixed Differential Equation with Piecewise Continuous Arguments

2018

apjm

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The paper focuses on the stability and oscillation of mixed differential equation with piecewise continuous arguments u (t) = au(t) + bu([t]) + cu(2[(t + 1)/2]). The explicit expression of the analytic solution, the conditions of stability and oscillation of the analytic solution are presented by the technique of solving differential equation, the theory of characteristic and the functional differential inequality, respectively. The results extend some existing ones.

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Section: Introductionmentioning

confidence: 99%

Stability and Oscillation of Mixed Differential Equation with Piecewise Continuous Arguments

2018

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“…The piecewise constant argument turns out to be one of various kinds of ‘memory’ effects on phase variables. The state history of these differential equations depends on some individual points, rather than on intervals (Alwan et al, 2013; Yu et al, 2016a). Since Shah and Wiener (1983) and Cooke and Wiener (1984) initiated the theory of differential equations with piecewise constant arguments, the theoretical results and the applications of these differential equations have been extensively investigated, including fuzzy neural networks (Bao et al, 2012), impulsive neural networks (Akhmet and Yilmaz, 2010, 2012; Yu and Cao, 2018) and biological systems (Öztük et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

Synchronization control of complex dynamical networks with piecewise constant arguments

2018

Transactions of the Institute of Measurement and Control

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The pinning synchronization problem is investigated for complex dynamical networks with hybrid coupling via impulsive control. Based on the Lyapunov stability theory, some novel synchronization criteria are derived and an impulsive pinning control law is proposed. By introducing a differential inequality for systems with piecewise constant arguments, it is not necessary to establish any relationship between the norms of the error states with or without piecewise constant arguments. Typical numerical examples are utilized to illustrate the validity and improvements as regards conservativeness of the theoretical results.

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“…In the literature, considerable work has been done on the qualitative investigation of EPCA, including the stability , the oscillation and the periodicity , and so forth. For more information on EPCA, we refer the interested reader to and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

Wang

2016

Numerical Methods Partial

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This article deals with the analytic and numerical stability of numerical methods for a parabolic partial differential equation with piecewise continuous arguments of alternately retarded and advanced type. First, application of the theory of separation of variables in matrix form and the Fourier method, the necessary and sufficient condition under which the analytic solution is asymptotically stable is derived. Then, the θ‐methods are applied to solve the corresponding initial value problem, the sufficient conditions for the asymptotic stability of numerical methods are obtained. Finally, several numerical examples are presented to support the theoretical results. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 531–545, 2017

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Comparison principle and stability of differential equations with piecewise constant arguments

Cited by 16 publications

References 19 publications

Stability and Oscillation of Mixed Differential Equation with Piecewise Continuous Arguments

Stability and Oscillation of Mixed Differential Equation with Piecewise Continuous Arguments

Synchronization control of complex dynamical networks with piecewise constant arguments

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

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