Global exponential convergence for a class of neutral functional differential equations with proportional delays

This paper is concerned with a class of non-autonomous neutral functional differential equations with multi-proportional delays. It is shown that all solutions of the addressed system are globally exponentially convergent by employing the differential inequality technique and a novel argument. The obtained results improve and supplement existing ones. We also use numerical simulations to demonstrate our theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  Hong Zhang,et al.  Global exponential stability of a delay reduced SIR model for migrant workers' home residence , 2015, Appl. Math. Lett..

[2]  Liqun Zhou,et al.  Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays , 2015, Neurocomputing.

[3]  Peng Ji-gen,et al.  Global asymptotic stability of CNNs with impulses and multi‐proportional delays , 2016 .

[4]  Yunkang Liu,et al.  The functional-differential equation y′( t )= A y ( t ) + B y ( qt ) + C y ′( qt ) + f ( t ) , 1998 .

[5]  Elena Braverman,et al.  On exponential stability of a linear delay differential equation with an oscillating coefficient , 2009, Appl. Math. Lett..

[6]  Graeme C. Wake,et al.  Holomorphic solutions to pantograph type equations with neutral fixed points , 2004 .

[7]  Bing Xiao,et al.  Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays , 2009, Appl. Math. Lett..

[8]  Krishnan Balachandran,et al.  EXISTENCE OF SOLUTIONS OF NONLINEAR FRACTIONAL PANTOGRAPH EQUATIONS , 2013 .

[9]  John Ockendon,et al.  The dynamics of a current collection system for an electric locomotive , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[10]  Alan Feldstein,et al.  On neutral functional-differential equations with variable time delays , 1998 .

[11]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[12]  Arieh Iserles,et al.  On Neutral Functional)Differential Equations with Proportional Delays , 1997 .

[13]  Liqun Zhou,et al.  Global exponential stability of cellular neural networks with multi-proportional delays , 2015 .

[14]  G. Derfel,et al.  On the asymptotics of solutions of a class of linear functional-differential equations , 1996 .

[15]  Yanli Xu.  Anti-periodic solutions for HCNNs with time-varying delays in the leakage terms , 2012, Neural Computing and Applications.

[16]  Zhiwen Long,et al.  New results on anti-periodic solutions for SICNNs with oscillating coefficients in leakage terms , 2016, Neurocomputing.

[17]  Bingwen Liu,et al.  Global exponential convergence of non-autonomous SICNNs with multi-proportional delays , 2017, Neural Computing and Applications.

[18]  Elena Braverman,et al.  New global exponential stability criteria for nonlinear delay differential systems with applications to BAM neural networks , 2013, Appl. Math. Comput..