Article
Mathematics, Applied
Krishnanand Vishwakarma, Moitri Sen
Summary: By studying the impact of hunting cooperation among predators and the Allee effect among prey on system dynamics, various bifurcations such as transcritical, saddle-node, Hopf, Bogdanov-Takens, and SN-TC have been observed. The analysis primarily focuses on the stability of coexisting equilibrium points, providing insights into how these phenomena affect the prey-predator system dynamics within the predator population.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Mathematics
Meng Zhu, Jing Li, Xinze Lian
Summary: This paper investigates a Leslie-Gower cross diffusion predator-prey model with a strong Allee effect and hunting cooperation. The effects of self diffusion and cross diffusion on the stability of the homogeneous state point and processes of pattern formation are mainly studied. The research shows that self diffusion and cross diffusion have important effects on the formation of spatial patterns.
Article
Mathematics, Applied
Ali Al Khabyah, Rizwan Ahmed, Muhammad Saeed Akram, Shehraz Akhtar
Summary: This work investigates the existence and topological classification of possible fixed points in a discrete predator-prey system with a strong Allee effect. Bifurcation theory and the center manifold theorem are used to explore the existence and direction of period-doubling and Neimark-Sacker bifurcations at the interior fixed point. A hybrid control method is employed to control chaos and bifurcations. Numerical examples are presented to verify the theoretical findings, revealing the complex dynamics of the discrete model. It is also shown that the system with the Allee effect takes a significantly longer time to reach its interior fixed point.
Article
Mathematics
Yining Xie, Jing Zhao, Ruizhi Yang
Summary: This paper proposes a diffusive predator-prey model with a strong Allee effect and nonlocal competition in the prey and a fear effect and gestation delay in the predator. The study mainly focuses on the local stability of the coexisting equilibrium and the existence and properties of Hopf bifurcation. Bifurcation diagrams with the fear effect parameter (s) and the Allee effect parameter (a) are provided, showing that the stable region of the coexisting equilibrium increases (or decreases) with an increase in the fear effect parameter (s) (or the Allee effect parameter (a)). The results demonstrate that the fear effect parameter (s), the Allee effect parameter (a), and gestation delay (t) can be utilized to control the growth of prey and predator populations.
Article
Chemistry, Multidisciplinary
Dingyong Bai, Jiaoxin Tang
Summary: In this study, a predator-prey system with cooperative hunting is investigated. The parameter space of the system is divided into several mutually exclusive regions. The dynamics of each parameter region are analyzed, and a complete description of the global dynamics is provided, including stability, Hopf bifurcation and its directions, and the existence of limit cycles. Comparing the dynamics of this system to that of a system without cooperative hunting reveals that cooperative hunting promotes the coexistence of prey and predator. When the predator mortality is low, hunting cooperation does not affect the population coexistence but it does affect the pattern of coexistence.
APPLIED SCIENCES-BASEL
(2023)
Article
Mathematics, Applied
Yudan Ma, Ming Zhao, Yunfei Du
Summary: In this study, a predator-prey model with strong Allee effect and Holling type II functional response is proposed and investigated. Through dynamical analysis, the existence of equilibria and bifurcations of the system are derived. It is found that the strong Allee effect plays a crucial role in the dynamics of the system.
Article
Mathematical & Computational Biology
Manoj K. Singh, Brajesh K. Singh, Poonam, Carlo Cattani
Summary: The effects of the strong Allee effect on the dynamics of the modified Leslie-Gower predator-prey model, in the presence of nonlinear prey-harvesting, have been investigated. The study found that the behaviors of the described mathematical model are positive and bounded for all future times. The conditions for the local stability and existence for various distinct equilibrium points have been determined.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mathematics
Maria Francesca Carfora, Isabella Torcicollo
Summary: A classical Lotka-Volterra model was extended in this study by introducing advection terms that included animal velocities. The effect of velocity on the problem's kinetics was analyzed. Traveling wave solutions were introduced to examine the behavior of species over time, and conditions for the coexistence or extinction of populations were found. Numerical simulations were conducted to illustrate the obtained results.
Article
Mathematics
Yanfei Du, Ben Niu, Junjie Wei
Summary: The paper investigates a diffusive predator-prey model with two delays, proving the existence of limit cycle in the weak cooperation model and identifying a loop of heteroclinic orbits connecting two equilibria by studying stable and unstable manifolds of saddles. When the conversion rate exceeds a threshold, both species go extinct.
Article
Mathematics
Liangying Miao, Zhiqian He
Summary: In this article, the authors investigate the Hopf bifurcation and Turing instability of a predator-prey model with hunting cooperation. The study analyzes the stability of the equilibrium and determines the conditions for the direction and stability of the bifurcating periodic solution. The results demonstrate the significant role of hunting cooperation in the model's dynamics, leading to beneficial effects on the predator population and increased Turing instability. Numerical simulations are utilized to visualize the complex dynamic behavior.
Article
Mathematics, Interdisciplinary Applications
Xiaoshuang Li, Danfeng Pang, Philip Wallhead, Richard Garth James Bellerby
Summary: This study investigates the impacts of ocean acidification and Allee effects on the dynamics of a marine predator-prey system. The study considers a diffusive predator-prey model with a double Allee effect on prey and a pH-dependent capture rate. The results show that changing environmental conditions can fundamentally alter the system dynamics, leading to decreased abundance and diversity of marine species by weakening predation rates. Additionally, the stability of periodic solutions is determined by double Allee effect parameters, with longer wavelengths observed as the Allee effect increases.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Interdisciplinary Applications
Yen-hsi Chou, Yunshyong Chow, Xiaochuan Hu, Sophia R-J Jang
Summary: This study shows that the number of equilibrium points in a predator-prey system depends on both the predator's basic reproduction number and the intensity of predator cooperation. While hunting cooperation can increase the likelihood of predator persistence, it may also destabilize the predator-prey interaction and drive the predator to extinction.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Engineering, Mechanical
Jianfeng Jiao, Can Chen
Summary: The paper studies the Bogdanov-Takens (B-T) bifurcation of a delayed predator-prey system with double Allee effect in prey. By analyzing the existence conditions of the B-T bifurcation, the associated generic unfolding and normal forms of the model at its interior equilibria are derived using the normal form theory and center manifold theorem for delay differential equations. The analysis of the topologically equivalent normal form system reveals that the Allee effect and delay can lead to various dynamic behaviors, providing insights into the potential mathematical mechanism driving population dynamics.
NONLINEAR DYNAMICS
(2021)
Article
Materials Science, Multidisciplinary
Nursanti Anggriani, Hasan S. Panigoro, Emli Rahmi, Olumuyiwa James Peter, Sayooj Aby Jose
Summary: This study examines a mathematical model of prey-predator interaction, incorporating the additive Allee effect and intraspecific competition on the predator. The Atangana-Baleanu-Caputo fractional derivative (ABC) is utilized to account for the memory effect on the model's behavioral dynamics. The model's feasibility and validity are confirmed through the existence, uniqueness, non-negativity, and boundedness of the solution. Equilibrium points at the origin, axial, and interior are identified, with their conditions of existence determined. The stability condition for each equilibrium point is investigated using the Lyapunov direct method for the ABC model. Numerical simulations are conducted to demonstrate the impact of various biological parameters on the solution dynamics. The emergence of transcritical, saddle-node, and backward bifurcations driven by the Allee constant leads to the occurrence of bistability conditions, while a Hopf bifurcation and the evolution of a limit-cycle are observed due to the memory effect. The biological interpretation of each analytical and numerical result illustrates how the population densities of both species continuously balance in their ecosystem.
RESULTS IN PHYSICS
(2023)
Article
Mathematics
Dingyong Bai, Xiaoxuan Zhang
Summary: This paper considers a predator-prey model where the prey's growth is affected by the additive predation of its potential predators. The model exhibits rich and complex dynamics, including the Allee effect, sensitivity to initial conditions, oscillatory behavior, and various bifurcations. The stability and bifurcation of the model with density dependent feedback time delay are investigated. The delay can destabilize the model and lead to bifurcation at both interior and boundary equilibria.
Article
Computer Science, Interdisciplinary Applications
Vitaly Chernik, Pavel Buklemishev
Summary: The paper introduces a simple 2D model for describing the cell motility on a homogeneous isotropic surface. The model incorporates the dynamics of complex actomyosin liquid, which affects the boundary dynamics and cell motility. It consists of a system of equations with a free boundary domain and includes a non-local term. The numerical solution of this model is presented in this work.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Hasan Karjoun, Abdelaziz Beljadid
Summary: In this study, we developed a numerical model based on the depth-averaged shallow water equations to simulate flows through vegetation field. The model takes into account the drag and inertia forces induced by vegetation, using different formulations for the stem drag coefficient. Turbulence induced by vegetation is also considered through the addition of diffusion terms in the momentum equations. The proposed numerical model is validated through numerical simulations and shows good accuracy in simulating overland flows under vegetation effects.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Bechir Naffeti, Hamadi Ammar, Walid Ben Aribi
Summary: This paper proposes a branch and bound multidimensional Holder optimization method, which converts a multivariate objective function into a single variable function and minimizes it using an iterative optimization method. The method is applied to solve a parameters identification problem resulting from the increase in infections, providing information about the prevalence and infection force.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Heba F. Eid, Erik Cuevas, Romany F. Mansour
Summary: The proposed modified Bonobo optimizer algorithm dynamically adjusts the trajectory of each search agent to overcome the flaw of the original algorithm and improve the performance and solution quality by exploring and exploiting different regions of the solution space.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Farshid Mehrdoust, Idin Noorani, Juho Kanniainen
Summary: This paper proposes a Markov-switching model to evaluate the dynamics of commodity futures and spot prices, and introduces a hidden Markov chain to model the sudden jumps in commodity prices. The model is calibrated using the crude oil spot price and estimation-maximization algorithm. The study also evaluates European call options written on crude oil futures under the regime-switching model and derives Greek formulas for risk assessment. The importance of this paper is rated at 8 out of 10.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Rupa Mishra, Tapas Kumar Saha
Summary: This paper presents a control scheme for distributed generation units to operate in stand-alone and grid-connected modes, with a smooth transition between the two. The control strategy includes predictive control for voltage and frequency regulation in stand-alone mode, and power control for symmetrical and unbalanced grid voltage conditions in grid-connected mode. The proposed control method improves power factor, reduces grid current harmonics, and eliminates grid frequency ripple.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Yu Wang, Yang Tian, Yida Guo, Haoping Wang
Summary: This paper proposes a multi-level control strategy for lower limb patient-exoskeleton coupling system (LLPECS) in rehabilitation training based on active torque. The controller consists of three sub-controllers: gait adjustment layer, interaction torque design layer, and trajectory tracking layer. The effectiveness of the proposed control strategy is demonstrated through co-simulations in the SimMechanics environment using an exoskeleton virtual prototype developed in SolidWorks.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Takuji Arai, Yuto Imai
Summary: The Barndorff-Nielsen and Shephard model is a jump-type stochastic volatility model, and this paper proposes two simulation methods for computing option prices under a representative martingale measure. The performance of these methods is evaluated through numerical experiments.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Wanai Li
Summary: This paper proposes a new framework that combines quadrature-based and quadrature-free discontinuous Galerkin methods and applies them to triangular and tetrahedral grids. Four different DG schemes are derived by choosing specific test functions and collocation points, improving computational efficiency and ease of code implementation.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Xiyuan Chen, Qiubao Wang
Summary: This paper introduces a technique that combines dynamical mechanisms and machine learning to reduce dimensionality in high-dimensional complex systems. The method utilizes Hopf bifurcation theory to establish a model paradigm and utilizes machine learning to train location parameters. The effectiveness and robustness of the proposed method are tested and validated through experiments and simulations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Muhammad Farman, Aqeel Ahmad, Anum Zehra, Kottakkaran Sooppy Nisar, Evren Hincal, Ali Akgul
Summary: Diabetes is a significant public health issue that affects millions of people worldwide. This study proposes a mathematical model to understand the mechanisms of glucose homeostasis, providing valuable insights for diabetes management. The model incorporates fractional operators and analyzes the impact of a new wave of dynamical transmission on equilibrium points, offering a comprehensive understanding of glucose homeostasis.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Gholamreza Shobeyri
Summary: This study introduces two improved Laplacian models for more accurate simulation of free surface flows in the context of the MPS method. The higher accuracy of these models compared to the traditional methods is verified through solving 2D Poisson equations and solving three benchmark free surface flow problems. These models can also resolve the issue of wave damping in the original MPS computations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Qiang Li, Jinling Liang, Weiqiang Gong, Kai Wang, Jinling Wang
Summary: This paper addresses the problem of nonfragile state estimation for semi-Markovian switching complex-valued networks with time-varying delay. By constructing an event-triggered generator and solving matrix inequalities, less conservative criteria are obtained, and the gains of the nonfragile estimator are explicitly designed. A numerical example is provided to demonstrate the effectiveness of the proposed estimation scheme.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Gengen Zhang, Jingyu Li, Qiong-Ao Huang
Summary: In this paper, a novel class of unconditionally energy stable schemes are constructed for solving gradient flow models by combining the relaxed scalar auxiliary variable (SAV) approach with the linear multistep technique. The proposed schemes achieve second-order temporal accuracy and strictly unconditional energy stability.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
S. Clain, J. Figueiredo
Summary: This study proposes a detailed construction of a very high-order polynomial representation and introduces a functional to assess the quality of the reconstruction. Several optimization techniques are implemented and their advantages in terms of accuracy and stability are demonstrated.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
