Hopf bifurcations of a ratio-dependent predator–prey model involving two discrete maturation time delays

To retard the onset of undesired bifurcation, the bifurcation control has developed into a theme of centralized research activities in delayed fractional-order system. In this paper, the problem of bifurcation control for a delayed fractional-order predator-prey model is investigated by employing an enhancing feedback control technique. The bifurcation point is firstly established for controlled model by using delay as a bifurcation parameter. Then, a series of numerical comparative studies on the effects of bifurcation control are implemented covering the partial or total removal of the branch for feedback gains. It reveals that the stability performance of the proposed model can be overwhelmingly elevated via the devised approaches in comparison with the dislocated feedback ones. A numerical example with simulations is ultimately designed to confirm the merits of the proposed theoretical results.

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“…In [42], the bifurcation of a ratio-dependent delayed predatorprey system with two delays was considered. The mathematical model was as follows:…”

Section: The Mathematical Modelmentioning

confidence: 99%

Fractional Dynamics Based-Enhancing Control Scheme of a Delayed Predator-Prey Model

et al. 2021

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“…The corresponding variance of fluctuations in Y(t) is given by (34) and the auto correlation function is the normalized auto covariance…”

Section: Stochastic Scenario Of Non-delayed Systemmentioning

confidence: 99%

“…Recently, Feng [33] studied the dynamics of a delayed ratio-dependent model with quadratic harvesting. Karaoglu and Merdan [34] studied a detailed Hopf-bifurcation analysis of a ratio-dependent predator-prey system involving two different discrete delays.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of generalist predator in a stochastic environment: Effect of delayed growth and prey refuge

Jana

Agrawal

Upadhyay

2015

Applied Mathematics and Computation

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“…Applying the local Hopf bifurcation theory, they analytically investigated the existence of periodic oscillations for (1), which depends on both the time delay and the market fraction of fundamentalists . Using the normal form theory and center manifold theorem (see also [15,16]), they derived the sufficient conditions to determine the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions.…”

Section: Introductionmentioning

confidence: 99%

Asset Price Dynamics in a Chartist-Fundamentalist Model with Time Delays: A Bifurcation Analysis

Dobrescu

Neamţu²,

Mircea³

2016

Discrete Dynamics in Nature and Society

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This paper studies the dynamic behavior of asset prices using a chartist-fundamentalist model with two speculative markets. To this effect, we employ a differential system with delays à la Dibeh (2007) to describe the price dynamics and we assume that the two markets are coupled via diffusive coupling terms. We study two different time delay cases, namely, when both markets experience the same time delay and when the time delay is different across markets. First, we theoretically determine that the equilibrium exists and investigate its stability. Second, we establish the general conditions for the existence of local Hopf bifurcations and analyze their direction and stability. The common conclusion from both the delay scenarios we consider is that coupled speculative markets with heterogeneous agents in each, but with different price dynamics, can be synchronized through diffusive coupling. Finally, we provide some numerical illustrations to confirm our theoretical findings.

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Hopf bifurcations of a ratio-dependent predator–prey model involving two discrete maturation time delays

Cited by 23 publications

References 21 publications

Fractional Dynamics Based-Enhancing Control Scheme of a Delayed Predator-Prey Model

Fractional Dynamics Based-Enhancing Control Scheme of a Delayed Predator-Prey Model

Dynamics of generalist predator in a stochastic environment: Effect of delayed growth and prey refuge

Asset Price Dynamics in a Chartist-Fundamentalist Model with Time Delays: A Bifurcation Analysis

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