THE CRITERIA FOR OSCILLATION OF TWO-DIMENSIONAL NEUTRAL DELAY DYNAMICAL SYSTEMS ON TIME SCALES

Zhongfeng Sun () and Huizeng Qin
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Zhongfeng Sun: Division of Dynamics and Control, School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong 255000, P. R. China
Huizeng Qin: Division of Dynamics and Control, School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong 255000, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 02, 1-12

Abstract: The neutral delay model has many applications in biology, ecology, man-made neural networks, mechanics and engineering. The main purpose of this paper is to establish new oscillation criteria for the two-dimensional neutral delay dynamical system zΔ(t) =b(t)g{r(t)ψ[x(t)]y[η(t)]},yΔ(t) = − f(t,x[δ(t)]), on a time scale 𠕋, where z(t) = x(t) + p(t)x[τ(t)] and a,r,p are positive rd-continuous functions, τ,δ,η : 𠕋 → 𠕋, are in accordance with the definition given by S. H. Saker, Oscillation of nonlinear dynamic equations on time scales, Appl. Math. Comput. 148 (2004) 81–91.

Keywords: Time Scales; Oscillation; Neutral Delay; Dynamic System; Riccati Transformation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400527

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