Multiple bifurcations in a mathematical model of glioma-immune interaction

Ma, Linyi; Hu, Dongpo; Zheng, Zhaowen; Ma, Cui‐Qin; Liu, Ming

doi:10.1016/j.cnsns.2023.107282

Cited by 5 publications

(3 citation statements)

References 43 publications

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“…For Equation (11), we obtain one of its exact solutions (x * , y * , h * f , k * f ) = (43.664637, 0.908638, 8.388521, 9.58437). Therefore, model ( 3 The continuation of the fold bifurcation curve for two control parameters k and h is drawn in Figure 1a.…”

Section: Fold-flip Bifurcationmentioning

confidence: 99%

“…In recent years, research on dynamical systems has undergone qualitative changes. Dynamical systems are an interdisciplinary field that can be applied not only to the study of epidemic diseases, but also to many other fields, such as predator-prey models [10] and tumor models [11]. For the research of epidemic diseases, we generally apply mathematical models to characterize their rich dynamic behavior [12].…”

Section: Introductionmentioning

confidence: 99%

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Codimension-Two Bifurcations of a Simplified Discrete-Time SIR Model with Nonlinear Incidence and Recovery Rates

Hu,

Liu,

et al. 2023

Mathematics

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In this paper, a simplified discrete-time SIR model with nonlinear incidence and recovery rates is discussed. Here, using the integral step size and the intervention level as control parameters, we mainly discuss three types of codimension-two bifurcations (fold-flip bifurcation, 1:3 resonance, and 1:4 resonance) of the simplified discrete-time SIR model in detail by bifurcation theory and numerical continuation techniques. Parameter conditions for the occurrence of codimension-two bifurcations are obtained by constructing the corresponding approximate normal form with translation and transformation of several parameters and variables. To further confirm the accuracy of our theoretical analysis, numerical simulations such as phase portraits, bifurcation diagrams, and maximum Lyapunov exponents diagrams are provided. In particular, the coexistence of bistability states is observed by giving local attraction basins diagrams of different fixed points under different integral step sizes. It is possible to more clearly illustrate the model’s complex dynamic behavior by combining theoretical analysis and numerical simulation.

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Section: Fold-flip Bifurcationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Codimension-Two Bifurcations of a Simplified Discrete-Time SIR Model with Nonlinear Incidence and Recovery Rates

Hu,

Liu,

et al. 2023

Mathematics

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“…In addition, high codimension bifurcation also plays an important role in the study of evolutionary biology and ecology. It has a wide range of applications in ecology, economics and other fields [3,25,32,36,43].…”

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confidence: 99%

High codimension bifurcations analysis in a predator-prey system with Michaelis-Menten type predator harvesting

Du,

Hu,

Zheng

et al. 2024

DCDS-B

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The main focus of this paper is to study some high codimension bifurcations of a predator-prey system with Michaelis-Menten type predator harvesting. In this paper, using the center manifold theorem, the cusp bifurcation of codimension two is discussed in detail. Furthermore, the Bautin bifurcation of codimension two and the Bogdanov-Takens bifurcation of codimension three are well studied by computing the second Lyapunov coefficient and using the normal form theory, respectively. Numerical simulations are provided to illustrate the theoretical results. The study of these bifurcations reveals the more complex dynamics of the system and may help us to better understand the complex interactions between predator and prey.

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A Mathematical Model for Assessing How Obesity-Related Factors Aggravate Diabetes

Jain,

Roy

2024

Acta Appl Math

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Multiple bifurcations in a mathematical model of glioma-immune interaction

Cited by 5 publications

References 43 publications

Codimension-Two Bifurcations of a Simplified Discrete-Time SIR Model with Nonlinear Incidence and Recovery Rates

Codimension-Two Bifurcations of a Simplified Discrete-Time SIR Model with Nonlinear Incidence and Recovery Rates

High codimension bifurcations analysis in a predator-prey system with Michaelis-Menten type predator harvesting

A Mathematical Model for Assessing How Obesity-Related Factors Aggravate Diabetes

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