Article
Mathematics
Ruizhi Yang, Xiao Zhao, Yong An
Summary: In this study, a delayed predator-prey model with diffusion and anti-predator behavior is investigated. The stability of the positive equilibrium is analyzed, and the existence of Hopf bifurcation is discussed based on the Hopf bifurcation theory. The properties of Hopf bifurcation are derived using the theory of center manifold and normal form method. Finally, the impact of time delay on the model is examined through numerical simulations.
Article
Mathematics, Applied
Guoshuang Wang, Jinfeng Wang
Summary: This paper deals with predator-prey models involving resource consumption and prey movement, subject to homogeneous Neumann boundary conditions. It demonstrates that global in time solutions are guaranteed for small prey movement coefficients in any spatial dimension. Furthermore, the homogeneous steady state remains globally stable with weak attractive prey movement sensitivity, while pattern formation can occur with repulsive prey movement sensitivity.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Mansoor Saburov
Summary: This paper explores the dichotomy of higher-order repeated time averages of a compact dynamical system in an infinite dimensional Banach space, as well as the uniformly historic behavior feature that leads to the non-existence of time averages. This feature ultimately results in the non-existence of higher-order repeated time averages.
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Liangying Miao, He Yang, Shengmao Fu
Summary: This paper investigates the global boundedness of a two-species predator-prey chemotaxis model with one signal. By establishing the uniform boundedness of the L-2-norm for prey and predator densities and the uniform boundedness of the L-4-norm for the signal gradient, the study considers the global existence and boundedness of classical solutions to the model in a three-dimensional bounded domain.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Mahmoud Moustafa, Farah Aini Abdullah, Sharidan Shafie
Summary: This article investigates a fractional-order prey-predator model with disease, predator prey harvesting, and interactions between species. The model is sensitive to fractional-order, prey harvesting, and initial conditions. Numerical simulations are used to illustrate theoretical findings.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Wentong Du, Min Xiao, Jie Ding, Yi Yao, Zhengxin Wang, Xinsong Yang
Summary: This paper proposes a delayed fractional-order predator-prey system with trans-species infectious diseases and implements the corresponding control strategy using fractional-order proportional-derivative (PD) control. The stability and bifurcation of the uncontrolled system are investigated, and the impacts of the controller on stability and bifurcation are explored. The effects of fractional order and control parameters on dynamics are also examined.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Applied
Jitsuro Sugie
Summary: Research on uniform global asymptotic stability predicts the asymptotic velocity to the origin for all solutions of equations describing nonlinear phenomena. This study provides sufficient conditions for uniform global asymptotic stability of the zero solution in a nonautonomous nonlinear dynamical system of second order. A first-order nonlinear differential equation associated with the second-order dynamical system is found to play a vital role in uniform global asymptotic stability. The proof involves careful tracking of the solutions of the dynamical system, and an example with a linear case is provided to illustrate the main result.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Yuxin Dong, Daiyong Wu, Chuansheng Shen, Luhong Ye
Summary: Experiments show that the fear of predators reduces the birth rate of the prey population, but it does not lead to their extinction. The sensitivity of the prey to predators affects the population density of both prey and predators. The introduction of saturated fear cost and predator-taxis sensitivity into the predator-prey interactions model proves to be feasible and provides insights into the stability of the model.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Interdisciplinary Applications
Shivam, Kuldeep Singh, Mukesh Kumar, Ramu Dubey, Teekam Singh
Summary: This paper conducts a temporal and spatio-temporal analysis of a prey-predator model with cooperative hunting among predators and herd behavior in prey. The findings reveal that cooperative hunting, interspecific competition, and self-diffusion have important implications in the prey-predator system.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Sangeeta Saha, Debgopal Sahoo, Guruprasad Samanta
Summary: Degradation of habitat caused by human activities, such as urbanization and industrial waste emission, poses severe challenges for the survival of living organisms. A study on prey-predator interaction with prey refuge shows that predators' survival is negatively affected when the rate of habitat destruction exceeds the rate of habitat regeneration. Even slightly lower rates of habitat degradation can still threaten predator species with extinction. Maintaining biodiversity requires efforts to slow down habitat degradation and accelerate habitat restoration, while effectively controlling habitat deterioration caused by human activity.
Article
Computer Science, Interdisciplinary Applications
Behzad Ghanbari, J. F. Gomez-Aguilar
Summary: This paper considers two accurate iterative methods for solving fractional differential equations with power law and Mittag-Leffler kernel, focusing on the stage-structured prey-predator model and several chaotic attractors. The results obtained show that both numerical methods are very efficient and provide precise and outstanding results for approximate numerical solutions of fractional differential equations with non-local singular kernels.
ENGINEERING WITH COMPUTERS
(2022)
Article
Biotechnology & Applied Microbiology
Arash Kheirodin, Pedro F. S. Toledo, Alvin M. Simmons, Jason M. Schmidt
Summary: Insect herbivore abundances in agricultural fields are influenced by the surrounding landscape complexity, which can regulate herbivore populations through direct and indirect effects. More research is needed to study how landscape complexity mediates multi-species interactions within fields.
BIOLOGICAL CONTROL
(2023)
Article
Engineering, Multidisciplinary
Kamal Shah, Thabet Abdeljawad, Fahd Jarad, Qasem Al-Mdallal
Summary: This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system using the conformable fractional order derivative (CFOD). The existence and uniqueness of at least one solution for the system are investigated using Schauder and Banach fixed point theorems. An algorithm for the approximate analytical solution is established using the conformable fractional differential transform (CFDT) technique. The results are simulated and compared with those obtained using the perturbation method for the Caputo fractional order derivative.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Biology
Claire Goiran, Terri Shine, Richard Shine
Summary: The evolution of bright warning colors in nontoxic animals is often attributed to mimicry of toxic species. By pulling snake-shaped models through the water and observing the response of predatory fish, the study found that banded color patterns reduce the vulnerability of non-venomous marine snakes to predation.
PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES
(2022)
Article
Mathematics, Applied
Xin Wang, Ruijing Li, Yu Shi
Summary: This paper studies a three-species predator-prey model with prey-taxis, where the prey exhibits taxis behavior during its movement. By proving the validity of certain conditions, the existence of at least one global generalized solution for the model is established.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
