Article
Computer Science, Interdisciplinary Applications
Balram Dubey, Sajan, Ankit Kumar
Summary: Recent studies show that prey population density is influenced by predator's direct killing and prey's fear response, leading to reduced reproduction rate and anti-predator behavior. The system exhibits bi-stability and Hopf-bifurcation, with delayed system showing chaotic behavior for large values of fear response delay. The findings are supported by numerical simulations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Computer Science, Interdisciplinary Applications
Nazmul Sk, Pankaj Kumar Tiwari, Samares Pal
Summary: In this study, the dynamics of a three species food chain model with hunting cooperation in predators and anti-predator behavior in prey population are examined. Results show that refuge plays a stabilizing role in the system, while hunting cooperation disrupts stability and leads to oscillations. Fear of middle-predator tends to stabilize the system, while fear of top-predator creates instability. Time delays in processes and seasonal forcing of parameters result in different types of periodic solutions and complex bursting patterns in the system.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Junli Liu, Bairu Liu, Pan Lv, Tailei Zhang
Summary: The proposed eco-epidemiological model in this paper considers the fear effect and hunting cooperation among predators on prey population and disease transmission. Mathematical analysis reveals the existence of backward bifurcation and bistability in the model, while numerical simulations demonstrate that low levels of fear and cooperation can stabilize the system but high levels may induce limit cycles.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Haokun Qi, Xinzhu Meng
Summary: In this study, we investigate the relationship between predator hunting and prey anti-predation behavior in the natural environment by considering a stochastic predator-prey model with fear effect and hunting cooperation, perturbed by nonlinear white noise. We first analyze the properties of the model's solutions and then provide sufficient conditions for extinction, persistence, and stationary distribution. We also establish the density function near the positive equilibrium of the model without white noise. Finally, we reveal through numerical simulations and theoretical analysis that fear effect, hunting cooperation, and white noise have essential influences on the dynamical behaviors of this model.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Mathematics, Interdisciplinary Applications
Renji Han, Subrata Dey, Malay Banerjee
Summary: In this work, the temporal and spatio-temporal dynamics of a prey-predator model with additive Allee effect and hunting cooperation among specialist predators are studied. The stability and existence of the coexistence equilibrium of the temporal model are affected by hunting cooperation. The temporal system exhibits a wide range of local bifurcations such as transcritical, saddle-node, Hopf, Bogdanov-Takens bifurcations, and a global Homoclinic bifurcation. For the diffusive system, well-posedness is proved, and Turing instability is investigated to understand the relationship between diffusion and hunting cooperation in stationary pattern formation. The main contribution of this work is the identification of all possible stationary patterns based on the signs of the coefficients in the amplitude equation.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Interdisciplinary Applications
Yuan Tian, Huanmeng Li, Kaibiao Sun
Summary: This study proposes a fishery model with dual effects of fear and cooperative hunting based on the cooperative hunting behaviors of predators and the fear response of prey in natural ecosystems. The impact of fear level and cooperative hunting intensity on the dynamics of the model is investigated. Additionally, a state-feedback intermittent fishing strategy is adopted for rational exploitation of fishery resources.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Mathematics, Interdisciplinary Applications
Sachin Bhalekar, Deepa Gupta
Summary: This study focuses on the stability analysis of a fractional order delay differential equation and provides linearized stability conditions. The stable region sketch in the q delta-plane is provided for any positive epsilon and p. Additionally, chaos in the proposed model is investigated for a wide range of delay parameter.
CHAOS SOLITONS & FRACTALS
(2022)
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
Computer Science, Interdisciplinary Applications
Krishnanand Vishwakarma, Moitri Sen
Summary: Cooperation among predator populations is a common phenomenon that can be considered as a type of Allee effect. Incorporating the Allee effect in prey populations can address complex dynamical features. Studying the dynamics of a generalist predator in prey-predator systems is also crucial in population research.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Engineering, Mechanical
Saswati Biswas, Pankaj Kumar Tiwari, Samares Pal
Summary: Fear of predation risk can have both beneficial and detrimental effects on prey animals, by limiting their exposure to potential predators and also by restricting their access to optimal resources. Research shows that the impact of fear on system stability has a threshold level, and considering factors like time lags and seasonal variations can add complexity to ecosystem dynamics. Chaotic behavior in the system can be suppressed by the time lag in fear effect on infection dynamics, offering important ecological insights into predator-prey interactions involving parasites.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Florent Feudjio Kemwoue, Vandi Deli, Helene Carole Edima, Joseph Marie Mendimi, Carlos Lawrence Gninzanlong, Mireille Mbou Dedzo, Jules Fossi Tagne, Jacques Atangana
Summary: In this study, a generic model of tumor growth with a delay distribution in the proliferation of tumor-stimulating effectors was investigated using analytical and numerical methods. The effects of delays on the dynamic stability of interactions between tumor, immune, and host cells were assessed. The results showed that delays can destabilize the system and induce chaotic behavior.
CHAOS SOLITONS & FRACTALS
(2022)
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, Applied
San-Xing Wu, Xin-You Meng
Summary: In this article, a delayed predator-prey system with fear effect, disease, and herd behavior in prey incorporating refuge is established. The stability and bifurcation of the system are discussed by analyzing characteristic equations and constructing a suitable Lyapunov function. Additionally, the impact of prey refuge, fear effect, and capture rate on the system is also considered in the analysis.
Article
Automation & Control Systems
Nguyen H. Du, Dang H. Nguyen, Nhu N. Nguyen, George Yin
Summary: This paper develops a new stability theory for stochastic functional differential systems with random switching, providing weaker and more verifiable conditions compared to previous literature. Examples and discussions are also included to demonstrate the applicability of the results.
Article
Mathematics, Interdisciplinary Applications
Sajan Balram Sajan, Balram Dubey, Sourav Kumar Sasmal
Summary: Plankton-fish interactions are a crucial topic in marine ecology. Besides direct predation, there are non-lethal implications in the relationship, such as reduced reproduction rate of zooplankton due to fear of predation. This study analyzes the role of fish-induced fear in zooplankton and its carry-over effects using a population model. The model considers functional responses to capture the interplay between phytoplankton, zooplankton, and fish. Theoretical analyses and numerical simulations reveal the impact of non-lethal parameters and fear on population densities. The study has significant implications for understanding nonlinear models in plankton-fish ecology.
CHAOS SOLITONS & FRACTALS
(2022)