Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect
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Sanaa Moussa Salman
Abstract
In this paper, we use new methods to investigate different bifurcations of fixed points in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect. The nonstandard discretization scheme produces a discrete analog of the continuous-time toxic-phytoplankton–zooplankton model with Allee effect. The local stability for proposed system around all of its fixed points is derived. We obtain the codimension-1 conditions of various bifurcations such as period doubling and Neimark–Sacker. Moreover, the system produces codimension-2 bifurcations such as resonance 1:1, 1:2, 1:3, and 1:4. Furthermore, the system can produce very rich dynamics, such as the existence of a semi-stable limit cycle, multiple coexisting periodic orbits, and chaotic behavior. Theoretical analysis is validated by numerical methods.
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Author contributions: Credit authorship contribution statement S. M. Salman Conceptualization, Methodology, Software, Formal analysis, Writing – original draft. A. A. Elsadany Investigation, Validation, Writing – review & editing.
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Research funding: This work has not been supported by any grants.
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Conflict of interest statement: The authors declare that they have no conflict of interest.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Article
- Hybrid solitary wave solutions of the Camassa–Holm equation
- Numerical simulations of wave propagation in a stochastic partial differential equation model for tumor–immune interactions
- A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation
- Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect
- Numerical modeling of the dam-break flood over natural rivers on movable beds
- A class of piecewise fractional functional differential equations with impulsive
- Lie symmetry analysis for two-phase flow with mass transfer
- Asymptotic behavior for stochastic plate equations with memory in unbounded domains
- Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay
- A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity
- Ground state solutions of Schrödinger system with fractional p-Laplacian
- Bifurcation analysis of a new stochastic traffic flow model
- An uncertainty measure based on Pearson correlation as well as a multiscale generalized Shannon-based entropy with financial market applications
- Hilfer fractional stochastic evolution equations on infinite interval
- Iterative learning control for conformable stochastic impulsive differential systems with randomly varying trial lengths
- Chebyshev wavelet-Picard technique for solving fractional nonlinear differential equations
- Theoretical assessment of the impact of awareness programs on cholera transmission dynamic
- Theoretical and numerical analysis of a prey–predator model (3-species) in the frame of generalized Mittag-Leffler law
- Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2
- Shehu transform on time-fractional Schrödinger equations – an analytical approach
- A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions
- Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary
Artikel in diesem Heft
- Frontmatter
- Original Research Article
- Hybrid solitary wave solutions of the Camassa–Holm equation
- Numerical simulations of wave propagation in a stochastic partial differential equation model for tumor–immune interactions
- A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation
- Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect
- Numerical modeling of the dam-break flood over natural rivers on movable beds
- A class of piecewise fractional functional differential equations with impulsive
- Lie symmetry analysis for two-phase flow with mass transfer
- Asymptotic behavior for stochastic plate equations with memory in unbounded domains
- Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay
- A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity
- Ground state solutions of Schrödinger system with fractional p-Laplacian
- Bifurcation analysis of a new stochastic traffic flow model
- An uncertainty measure based on Pearson correlation as well as a multiscale generalized Shannon-based entropy with financial market applications
- Hilfer fractional stochastic evolution equations on infinite interval
- Iterative learning control for conformable stochastic impulsive differential systems with randomly varying trial lengths
- Chebyshev wavelet-Picard technique for solving fractional nonlinear differential equations
- Theoretical assessment of the impact of awareness programs on cholera transmission dynamic
- Theoretical and numerical analysis of a prey–predator model (3-species) in the frame of generalized Mittag-Leffler law
- Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2
- Shehu transform on time-fractional Schrödinger equations – an analytical approach
- A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions
- Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary
