Bifurcation analysis of a two‐dimensional discrete‐time predator–prey model

Hamada, M. Y.; El‐Azab, Tamer; El-Metwally, H.

doi:10.1002/mma.8807

Cited by 14 publications

(2 citation statements)

References 38 publications

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“…This decision is taken by considering the mathematical aspect rather than its biological meanings. The discrete-time model has some advantages rather than its continuous ones, such as complexity in dynamical behaviors and suitability for approximating the real data since data has discrete formulae [16][17][18]. By using the forward Euler method as in [19], we obtain the following discrete- 4) with parameter values given by eq.…”

Section: Introductionmentioning

confidence: 99%

The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting

et al. 2023

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Modeling the interaction between prey and predator plays an important role in maintaining the balance of the ecological system. In this paper, a discrete-time mathematical model is constructed via a forward Euler scheme, and then studied the dynamics of the model analytically and numerically. The analytical results show that the model has two fixed points, namely the origin and the interior points. The possible dynamical behaviors are shown analytically and demonstrated numerically using some phase portraits. We show numerically that the model has limit-cycles on its interior. This guarantees that there exists a condition where both prey and predator maintain their existence periodically.

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Section: Introductionmentioning

confidence: 99%

The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting

et al. 2023

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“…These methods, however, are not dynamically consistent with their continuous counterparts. Some recent works on discrete-time models can be found in, among many others, [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics and chaos control in a nonlinear discrete prey–predator model

Mokni¹,

Ali²,

Ch-Chaoui³

2023

Math. Model. Comput.

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The dynamics of prey–predator interactions are often modeled using differential or difference equations. In this paper, we investigate the dynamical behavior of a two-dimensional discrete prey–predator system. The model is formulated in terms of difference equations and derived by using a nonstandard finite difference scheme (NSFD), which takes into consideration the non-overlapping generations. The existence of fixed points as well as their local asymptotic stability are proved. Further, it is shown that the model experiences Neimark–Sacker bifurcation (NSB for short) and period-doubling bifurcation (PDB) in a small neighborhood of the unique positive fixed point under certain parametric conditions. This analysis utilizes bifurcation theory and the center manifold theorem. The chaos produced by NSB and PDB is stabilized. Finally, we use numerical simulations and computer analysis to check our theories and show more complex behaviors.

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Investigating the dynamics of generalized discrete logistic map

Hamada

2024

Math Methods in App Sciences

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In recent years, conventional logistic maps have been applied across various fields including modeling and security, owing to their versatility and utility. However, their reliance on a single modifiable parameter limits their adaptability. This paper aims to explore generalized logistic maps with arbitrary powers, which offer greater flexibility compared to the standard logistic map. By introducing additional parameters in the form of arbitrary powers, these maps exhibit increased degrees of freedom, thus expanding their applicability across a wider spectrum of scenarios. Consequently, the conventional logistic map emerges as a specific instance within the proposed framework. The inclusion of arbitrary powers enriches system dynamics, enabling a more nuanced exploration of system behavior in diverse contexts. Through a series of illustrations, this study investigates the influence of arbitrary powers and equation parameters on equilibrium points, their positions, stability conditions, basin of attraction, and bifurcation diagrams, including the emergence of chaotic behavior.

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Bifurcation analysis of a two‐dimensional discrete‐time predator–prey model

Cited by 14 publications

References 38 publications

The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting

The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting

Complex dynamics and chaos control in a nonlinear discrete prey–predator model

Investigating the dynamics of generalized discrete logistic map

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