Article
Mathematics, Interdisciplinary Applications
Fatao Wang, Ruizhi Yang
Summary: In this paper, we investigate a cross-diffusion predator-prey system with Holling type functional response. We analyze the local stability, Turing instability, spatial pattern formation, Hopf and Turing-Hopf bifurcation of the equilibrium. Numerical simulation reveals that the system experiences cross-diffusion-driven instability and exhibits various patterns such as spots, stripe-spot mixtures, and labyrinthine patterns. The study also shows that the intrinsic growth rate coefficient and the environmental carrying capacity coefficient are crucial factors for the stability of the predator-prey system.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Henan Wang, Ping Liu
Summary: In this paper, a diffusive predator-prey model with Allee effect and generalized Holling type IV functional response is established. The complex pattern dynamics and bifurcation phenomena of the system are analyzed using linear stability analyses and bifurcation theory. The conditions for Hopf instability, Turing instability, and Hopf-Turing instability of constant positive steady solutions are presented for spiral pattern, spot pattern or spot-stripe mix pattern, and chaotic pattern, respectively. The impacts of Allee effect and cross-diffusion on pattern formations are discussed, and numerical simulations are provided to demonstrate the theoretical results in two spatial dimensions. It is found that a larger Allee effect constant A and cross-diffusion coefficient d4 promote the formation of Turing pattern, while the cross-diffusion coefficient d3 suppresses its formation.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematical & Computational Biology
Subrata Dey, Malay Banerjee, Saktipada Ghorai
Summary: A prey-predator model with a generalist predator and Holling type-II functional response exhibits complex dynamics, including bistability, tristability, and various global and local bifurcations. The presence of a generalist predator reduces predation pressure on the focal prey species, leading to increased stability. The model also shows the existence of steady state solutions for suitable parameter values in a spatio-temporal diffusive system. Weakly nonlinear analysis and numerical simulations confirm the analytical results and identify bifurcations of stable stationary patch solutions and dynamic pattern solutions in the Turing and Turing-Hopf regions.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
(2022)
Article
Engineering, Mechanical
Mengxin Chen
Summary: This paper investigates the spatiotemporal inhomogeneous pattern phenomenon of a predator-prey model with chemotaxis and time delay. The study provides sufficient conditions to ensure the existence of Turing instability by adjusting the control parameters of time delay and chemotaxis. It also determines the occurrence conditions of Turing-Hopf bifurcation using time delay control parameter and chemotaxis sensitivity coefficient. The research shows that both time delay and chemotaxis can affect the formation of spatiotemporal inhomogeneous patterns.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Mengxin Chen
Summary: In this paper, the spatiotemporal inhomogeneous pattern phenomenon of a predator-prey model with chemotaxis and time delay is investigated. The precise intervals of the Turing instability are determined, and sufficient conditions for its existence are obtained by adjusting the control parameters. Numerical experiments show that both the time delay control parameter and chemotaxis sensitivity coefficient can affect the formation of the patterns.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Jia Liu, Jing Chen, Canrong Tian
Summary: By introducing a weighted networked structure and analyzing the amplitude equation, this study investigates the Turing bifurcation in the classical reaction-diffusion system, demonstrating its existence with large diffusion rates and stability. The findings suggest the importance of network structures in understanding complex dynamics in reaction-diffusion systems.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Interdisciplinary Applications
Malay Banerjee, Swadesh Pal, Pranali Roy Chowdhury
Summary: This paper investigates the spatio-temporal pattern formation in a complex habitat. The results show that the shape and size of the habitat play a significant role in determining the spatio-temporal patterns.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics
Ruizhi Yang, Qiannan Song, Yong An
Summary: This paper considers a diffusive predator-prey system with a functional response that increases in both predator and prey densities. The Turing instability and Hopf bifurcation are studied by analyzing the characteristic roots of the system. By calculating the normal form of the Turing-Hopf bifurcation and conducting numerical simulations, the dynamic properties of different types of solutions in each parameter region of the phase diagram are found to be extremely rich.
Article
Mathematics, Applied
Fethi Souna, Pankaj Kumar Tiwari, Mustapha Belabbas, Youssaf Menacer
Summary: In this paper, the intrinsic impact of the predator-taxis coefficient on the formation of spatial patterns in a predator-prey system with prey social behavior subject to Neumann boundary conditions is investigated. The Turing pattern is found to be fully captured by three distinct critical thresholds, and the direction of Turing bifurcation is established through weakly nonlinear analysis and the amplitude equation. The mathematical analysis reveals that the inclusion of the predator-taxis coefficient in the predator-prey system may lead to the emergence of either subcritical or supercritical Turing bifurcation. Numerical experiments confirm the theoretical findings and exhibit various spatial patterns with different values of predator-taxis coefficients.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Linhe Zhu, Le He
Summary: The paper presents an example of a reaction-diffusion model defined on continuous space to study common problems under Turing instability. It analyzes the necessary conditions for Turing instability and the theoretical conditions for the appearance of specific patterns near Turing bifurcation. The numerical simulations confirm the correctness of the theoretical analysis and find that the pattern type can be changed by the cross-diffusion coefficient.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Yehu Lv, Zhihua Liu
Summary: In this paper, a diffusive Brusselator model with gene expression time delay is proposed and its bifurcation behavior is studied. The conditions for Turing instability are derived, and the spatiotemporal dynamics in six different regions of the parameter plane are analyzed.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Q. I. N. G. Y. A. N. Shi, Y. O. N. G. L. Song
Summary: This paper proposes a diffusive model with nonlocal memory-based diffusion to model animal movement. The stability of the positive homogeneous steady state and the bifurcation behaviors are investigated by taking the memory delay and the memory-based diffusion coefficient as bifurcation parameters. Rich dynamics in the system are observed, including Turing bifurcations and Hopf bifurcations.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2023)
Article
Physics, Mathematical
Eddie Nijholt, Tiago Pereira, Fernando C. Queiroz, Dmitry Turaev
Summary: We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. We give general conditions for the existence of chaotic network dynamics under homogeneous diffusive coupling for any network configuration. Our method is based on the theory of local bifurcations developed for diffusively coupled networks. In particular, we introduce the class of versatile network configurations and prove that the Taylor coefficients of the reduction to the center manifold can take any given value for any versatile network.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
Yu Mu, Wing-Cheong Lo
Summary: In this paper, the dynamics of competitive species in spatial domains are investigated, where populations compete for resources and diffuse. The presence of diffusion and stimulating chemicals in the competitive system is considered. The study shows the existence of a positive steady-state and explores the impact of diffusion and stimulating substances on species concentration dynamics. Furthermore, the diffusion phenomenon leads to Turing instability and non-homogeneous spatial distribution of species concentration. Several numerical examples are provided to validate the theoretical findings.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics
Gui-Quan Sun, Hong-Tao Zhang, Yong-Li Song, Li Li, Zhen Jin
Summary: The study investigates the spatiotemporal dynamics of a diffusive plant-water model in an arid flat environment and finds that the system exhibits Turing-Hopf bifurcation properties. By analyzing the normal form theory of reaction-diffusion equations, the study reveals that tiny changes in parameters can induce the switch between different states, including uniform state, time periodic state, spatially inhomogeneous steady state, and spatially inhomogeneous periodic state.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Engineering, Multidisciplinary
Pranali Roy Chowdhury, Malay Banerjee, Sergei Petrovskii
Summary: This study investigates a new ecological dynamics model that combines multiple timescales and ratio-dependent predator responses, conducting analyses and numerical simulations in both nonspatial and spatial cases to reveal various characteristics of the model.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mathematics, Interdisciplinary Applications
Malay Banerjee, Swadesh Pal, Pranali Roy Chowdhury
Summary: This paper investigates the spatio-temporal pattern formation in a complex habitat. The results show that the shape and size of the habitat play a significant role in determining the spatio-temporal patterns.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Dongdong Ni, Wanbiao Ma, Malay Banerjee
Summary: In this paper, a size-structured PDE model considering the size of algae cells is established, which depicts the evolutionary relationship of the growth of algae cells, the nutrient absorption, and flocculation effect. The numerical observation shows that the model has complex dynamics, such as the appearances of backward bifurcation of equilibrium states and bistability. The main theoretical results include the well-posedness of the solution, the existence and local stability condition of the coexistence equilibrium state of algae, and the global stability condition of the algae-free equilibrium state.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Pranali Roy Chowdhury, Malay Banerjee, Sergei Petrovskii
Summary: In this paper, a generalized version of the Hastings-Powell model is studied, which includes intra-specific competition among predators and top predators and incorporates different timescales for different species. The results show that the dynamics of the system are more complex than previously observed, with the potential for bi-stability or tri-stability. The impact of intra-specific competition on the system's dynamics is also investigated.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Biology
Samiran Ghosh, Vitaly Volpert, Malay Banerjee
Summary: The study focuses on a new immuno-epidemiological model that considers recovery and death rates as functions of time after infection onset. The disease transmission rate depends on the viral load within individuals, determined by an immunological submodel. The age-dependent model considers viral load, recovery and death rates as functions of age, treated as a continuous variable. Equations for susceptible, infected, recovered and dead compartments are expressed in terms of the number of newly infected cases. The model's analysis includes proving the existence and uniqueness of a solution. Additionally, it shows how the model can be simplified under certain assumptions on recovery and death distributions to age-dependent SIR or delay models. The model is validated using COVID-19 case data, revealing that the proportion of young age groups can significantly impact the epidemic progression due to their higher disease transmission rate compared to other age groups.
JOURNAL OF MATHEMATICAL BIOLOGY
(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
Mathematics, Interdisciplinary Applications
Malay Banerjee, Samiran Ghosh, Piero Manfredi, Alberto d'Onofrio
Summary: This study proposes a spatio-temporal behavioral epidemiology model where vaccine propensity depends on non-local information. The study reveals that vaccine hesitancy can induce the onset of various dynamic patterns relevant to epidemiology, including behavior-modulated patterns and spatio-temporal chaos.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Pranali Roy Chowdhury, Sergei Petrovskii, Vitaly Volpert, Malay Banerjee
Summary: The spatio-temporal complexity of ecological dynamics has been a focus of research, with pattern formation and chaos observed in field data. The elementary prey-predator system has been shown to contribute to ecological dynamical complexity. This paper examines the effect of intraspecific competition in the predator population using Bazykin's model. The study explores the slow-fast dynamics and analyzes the existence of Turing bifurcation and corresponding spatial patterns.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Chemistry, Physical
Suniksha Gupta, Smita Howlader, Satyavir Singh, Atul Sharma, K. Asokan, M. K. Banerjee, K. Sachdev
Summary: This study investigates the impact of N-ion implantation on the structure and properties of Mg2Si thin films. The results show that ion irradiation causes partial amorphization of the film and particle coarsening. Electrical measurements reveal an increase in conductivity with increasing ion fluence.
Article
Mathematics, Applied
Jyotirmoy Roy, Malay Banerjee
Summary: This article investigates the proof of global stability for unique locally stable coexistence equilibrium points in predator-prey models. The authors prove the global stability of the coexistence equilibrium point in a predator-prey model with a generalist predator using a suitable Lyapunov function and the Bendixson-Dulac criteria, as well as in the corresponding delayed model with maturation delay using a Lyapunov functional and LaSalle's invariance principle.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Biology
Subrata Dey, S. Ghorai, Malay Banerjee
Summary: The Allee effect in population dynamics has a significant impact on suppressing the paradox of enrichment and can lead to highly complex dynamics. This study investigates the influence of the reproductive Allee effect on the growth rate of prey in a prey-predator model with Beddington-DeAngelis functional response. Local and global bifurcations are identified, and the existence of heterogeneous steady-state solutions in the spatio-temporal system is established for suitable parameter ranges. The inclusion of the reproductive Allee effect destabilizes the coexistence equilibrium and generates various stationary solutions and complex dynamic patterns.
JOURNAL OF MATHEMATICAL BIOLOGY
(2023)
Article
Computer Science, Interdisciplinary Applications
Jyotirmoy Roy, Subrata Dey, Malay Banerjee
Summary: Discrete time delay is widely used in models of interacting populations to capture various biological processes. The primary goal of this article is to explore how delayed maturity in generalist predators qualitatively affects the dynamics of a predator-prey system. The analysis demonstrates that delayed maturation of generalist predators promotes stable coexistence.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Physics, Fluids & Plasmas
Suresh Kumarasamy, Malay Banerjee, Vaibhav Varshney, Manish Dev Shrimali, Nikolay V. Kuznetsov, Awadhesh Prasad
Summary: Hidden attractors, which are not associated with equilibria, are present in many nonlinear dynamical systems and are difficult to locate. This research letter presents the route to hidden attractors in systems with stable equilibrium points and in systems without any equilibrium points. The study shows that hidden attractors emerge as a result of the saddle-node bifurcation of stable and unstable periodic orbits. Real-time hardware experiments were conducted to demonstrate the existence of hidden attractors in these systems. The findings provide insights into the generation of hidden attractors in nonlinear dynamical systems.
Article
Physics, Multidisciplinary
S. Gupta, M. K. Gupta, D. C. C. Sharma, M. Kr Chowrasia, M. K. Banerjee
Summary: Silver telluride (Ag2Te) thin films of different thicknesses were prepared by thermal evaporation technique and characterized using XRD, SEM, EDAX, and UV spectroscopy. The results showed that films with thickness above 100 nm were crystalline, while lower thickness films were amorphous. The UV spectroscopy indicated that the band gap of Ag2Te thin films ranged from 1.4 to 1.7 eV, and the films demonstrated high absorption coefficient in the UV region. The I-V characteristics study suggested that the Ag2Te thin films were highly conducting and could be a potential material for solar cell application.
INDIAN JOURNAL OF PHYSICS
(2023)
Article
Energy & Fuels
Mukesh Kumar Gupta, Krishna Kumar Sinha, Rahul Kumar, M. K. Banerjee
Summary: The present paper assesses the water treatment capacity of a solar system with special features and investigates its efficacy in reducing TDS content and managing water contaminants. The results show that the solar system efficiently purifies contaminated water, with a slight advantage for the coupled system over the standalone system.
INTERNATIONAL JOURNAL OF RENEWABLE ENERGY RESEARCH
(2022)
