Delay induced multiple stability switch and chaos in a predator–prey model with fear effect

Panday, Pijush; Samanta, Sudip; Pal, Nikhil R.; Chattopadhyay, Joydev

doi:10.1016/j.matcom.2019.12.015

“…Furthermore, chaos is related to how a deterministic dynamical system can be potentially unpredictable due to an extreme sensitivity to initial conditions, which is also known as the "Butterfly Effect" [259]. Chaos has been observed in many different phenomena, including electric circuits [260][261][262], weather [263][264][265], physiological systems [266][267][268], financial markets [269][270][271], complex networks [272], the serrated flow in alloys [116,216,273], and ecological systems [274][275][276].…”

Section: Chaos Analysismentioning

confidence: 99%

A Review of the Serrated-Flow Phenomenon and Its Role in the Deformation Behavior of High-Entropy Alloys

Brechtl

¹

,

Chen

²

,

Lee

³

et al. 2020

Metals

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High-entropy alloys (HEAs) are a novel class of alloys that have many desirable properties. The serrated flow that occurs in high-entropy alloys during mechanical deformation is an important phenomenon since it can lead to significant changes in the microstructure of the alloy. In this article, we review the recent findings on the serration behavior in a variety of high-entropy alloys. Relationships among the serrated flow behavior, composition, microstructure, and testing condition are explored. Importantly, the mechanical-testing type (compression/tension), testing temperature, applied strain rate, and serration type for certain high-entropy alloys are summarized. The literature reveals that the serrated flow can be affected by experimental conditions such as the strain rate and test temperature. Furthermore, this type of phenomenon has been successfully modeled and analyzed, using several different types of analytical methods, including the mean-field theory formalism and the complexity-analysis technique. Importantly, the results of the analyses show that the serrated flow in HEAs consists of complex dynamical behavior. It is anticipated that this review will provide some useful and clarifying information regarding the serrated-flow mechanisms in this material system. Finally, suggestions for future research directions in this field are proposed, such as the effects of irradiation, additives (such as C and Al), the presence of nanoparticles, and twinning on the serrated flow behavior in HEAs.

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“…In what follows, we present the computation of these coefficients at the equilibria E in and E 2 (u * 2 , 0), respectively. The calculation process is similar to that in many references (see, e.g., [41][42][43][44][45]).…”

Section: Direction and The Stability Of Hopf-bifurcating Periodic Sol...mentioning

confidence: 94%

Dynamics of a Predator–Prey Model with the Additive Predation in Prey

Bai

¹

,

Zhang

²

2022

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In this paper, we consider a predator–prey model, in which the prey’s growth is affected by the additive predation of its potential predators. Due to the additive predation term in prey, the model may exhibit the cases of the strong Allee effect, weak Allee effect and no Allee effect. In each case, the dynamics of global features of the model are investigated. Compared to the well-known Lotka–Volterra type model, the model proposed in this paper exhibits much richer and more complex dynamic behaviors, such as the Allee effect, the sensitivity to the initial conditions caused by the strong Allee effect, the oscillatory behavior and the Hopf and heteroclinic bifurcations. Furthermore, the stability and Hopf bifurcation of the model with the density dependent feedback time delay in prey are investigated. By the normal form method and center manifold theory, the explicit formulas are presented to determine the direction of Hopf bifurcation and the stability and period of Hopf-bifurcating periodic solutions. Theoretical analysis and numerical simulation indicate that the delay may destabilize the model, and cause the Hopf bifurcation not only at the interior equilibrium but also at a boundary equilibrium.

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“…Furthermore, chaos is related to how a deterministic dynamical system can be potentially unpredictable due to an extreme sensitivity to initial conditions, which is also known as the "Butterfly Effect" [259]. Chaos has been observed in many different phenomena, including electric circuits [260][261][262], weather [263][264][265], physiological systems [266][267][268], financial markets [269][270][271], complex networks [272], the serrated flow in alloys [116,216,273], and ecological systems [274][275][276].…”

Section: Chaos Analysismentioning

confidence: 99%

Complex Concentrated Alloys (CCAs)

2020

0

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Delay induced multiple stability switch and chaos in a predator–prey model with fear effect

Cited by 73 publications

References 53 publications

A Review of the Serrated-Flow Phenomenon and Its Role in the Deformation Behavior of High-Entropy Alloys

A Review of the Serrated-Flow Phenomenon and Its Role in the Deformation Behavior of High-Entropy Alloys

Dynamics of a Predator–Prey Model with the Additive Predation in Prey

Complex Concentrated Alloys (CCAs)

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