On the Asymptotic Behavior of a Class of Second-Order Non-Linear Neutral Differential Equations with Multiple Delays

The oscillation of impulsive differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of impulsive differential equations. In this work, several sufficient conditions are established for oscillatory or asymptotic behavior of second-order neutral impulsive differential systems for various ranges of the bounded neutral coefficient under the canonical and non-canonical conditions. Here, one can see that if the differential equations is oscillatory (or converges to zero asymptotically), then the discrete equation of similar type do not disturb the oscillatory or asymptotic behavior of the impulsive system, when impulse satisfies the discrete equation. Further, some illustrative examples showing applicability of the new results are included.

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“…By (A5), we can assume ν(ς(λ)) > 0 for λ ≥ λ 1 . From (E) and (A4), we get (11). Consequently, r f is non-increasing on [λ 1 , ∞).…”

Section: Oscillation Under Non-canonical Conditionsmentioning

confidence: 91%

New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions

et al. 2021

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“…Finally, we refer the interested reader to the following paper and to the references therein for some recent results on the oscillation theory for ordinary differential equations of several orders [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Some conditions for the oscillation of second-order differential equations with several mixed delays

Santra

Scapellato

2022

J. Fixed Point Theory Appl.

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“…In contrast, the nonlinear approach can capture the features of economic and financial series and their sudden fluctuations, and hence plays a relevant role in economic modeling [32]. Likewise, dynamical systems involving time delays have applications in a number of fields such as biology, population dynamics and economics [33]. The delayed model can produce oscillating trajectories for the solutions under certain conditions and explain the business cycles [34,35].…”

Section: Introductionmentioning

confidence: 99%

A Chaos Analysis of the Dry Bulk Shipping Market

Inglada-Pérez

Coto-Millán

2021

Mathematics

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Finding low-dimensional chaos is a relevant issue as it could allow short-term reliable forecasting. However, the existence of chaos in shipping freight rates remains an open and outstanding matter as previous research used methodology that can produce misleading results. Using daily data, this paper aims to unveil the nonlinear dynamics of the Baltic Dry Index that has been proposed as a measure of the shipping rates for certain raw materials. We tested for the existence of nonlinearity and low-dimensional chaos. We have also examined the chaotic dynamics throughout three sub-sampling periods, which have been determined by the volatility pattern of the series. For this purpose, from a comprehensive view we apply several metric and topological techniques, including the most suitable methods for noisy time series analysis. The proposed methodology considers the characteristics of chaotic time series, such as nonlinearity, determinism, sensitivity to initial conditions, fractal dimension and recurrence. Although there is strong evidence of a nonlinear structure, a chaotic and, therefore, deterministic behavior cannot be assumed during the whole or the three periods considered. Our findings indicate that the generalized autoregressive conditional heteroscedastic (GARCH) model and exponential GARCH (EGARCH) model explain a significant part of the nonlinear structure that is found in the dry bulk shipping freight market.

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On the Asymptotic Behavior of a Class of Second-Order Non-Linear Neutral Differential Equations with Multiple Delays

Cited by 18 publications

References 46 publications

New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions

New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions

Some conditions for the oscillation of second-order differential equations with several mixed delays

A Chaos Analysis of the Dry Bulk Shipping Market

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