Slowly oscillating solutions in a class of second-order discontinuous delayed systems

Li, Liping; Zhao, Zhenjiang

doi:10.1007/s11071-018-4363-2

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…Oscillatory behaviors of Eq. (1.1) with finite frequency (i.e., many finite zeros in any bounded time interval) have been extensively studied; for instance, see [8][9][10][11][12]. Most of the related results mainly focus on the existence, uniqueness, and stability of slowly or rapidly periodic oscillatory.…”

Section: Introductionmentioning

confidence: 99%

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Infinite Frequency Oscillations in a Class of Discontinuous Systems with a Variable Delay

Li¹

2022

Preprint

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This paper mainly investigates the oscillatory behaviors in a class of discontinuous dynamical systems with a variable delay. Under the restrictions of boundedness and monotonicity on the time-delay function, the type and distribution of zero points of the solution are firstly determined. And then, the non-existence of oscillatory solutions with infinite frequency is proven for the systems with two classes of discontinuous vector fields. In detail, by applying the inequality techniques on a backward shift operator, an exact lower bound of the time is provided to ensure the vanishing of infinite frequency oscillations after this time. The obtained results improve some previous work in the cases of the constant delay and constant vector fields.

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Section: Introductionmentioning

confidence: 99%

“…According to Fig. 1, we know 11 3 ≤ τ (t) ≤ 8 as t ≥ 0, and that t − τ (t) is strictly increasing on [16n, 16(n + 1))(n = 0, 1, 2, • • • ). It is easy to verify that Eq.…”

Section: Introductionmentioning

confidence: 99%

Infinite Frequency Oscillations in a Class of Discontinuous Systems with a Variable Delay

Li¹

2022

Preprint

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Infinite Frequency Oscillations in a Class of Discontinuous Equations with a Variable Delay

2022

J Dyn Diff Equat

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Periodic motions in a class of discontinuous delayed systems with a parabolic boundary

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Various periodic motions are investigated for a mass-spring-damper oscillator described by second-order discontinuous delayed systems with a parabolic boundary. The [Formula: see text]-function related to a delayed variable is first developed to judge the crossing, sliding, and grazing motions at the boundary points. Then, basic and local mappings, together with their motion equations, are classified by current and delayed states of a local flow. It is shown that periodic motions can be predicted analytically in terms of the return mapping and the initial value function provided posteriorly. Finally, numerical simulations are given to illustrate the existence of slowly oscillating periodic solutions without or with sliding portions as well as a crossing periodic solution not slowly oscillating. These results not only enrich and extend switchability theory of discontinuous delayed systems, but also reveal some complicated periodic behaviors which cannot be found in continuous delayed systems and discontinuous systems without time delay.

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Slowly oscillating solutions in a class of second-order discontinuous delayed systems

Cited by 4 publications

References 25 publications

Infinite Frequency Oscillations in a Class of Discontinuous Systems with a Variable Delay

Infinite Frequency Oscillations in a Class of Discontinuous Systems with a Variable Delay

Infinite Frequency Oscillations in a Class of Discontinuous Equations with a Variable Delay

Periodic motions in a class of discontinuous delayed systems with a parabolic boundary

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