Bifurcation structure of coexistence states for a prey–predator model with large population flux by attractive transition

2021 ◽  
pp. 1-24
Author(s):  
Kousuke Kuto ◽  
Kazuhiro Oeda
Keyword(s):  
Positive Solutions ◽  
Large Population ◽  
Global Bifurcation ◽  
Competition Model ◽  
The Other ◽  
Bifurcation Structure ◽  
Nonlinear Anal ◽  
Connected Set ◽  
Coexistence States ◽  
Predator Model

This paper is concerned with a prey–predator model with population flux by attractive transition. Our previous paper (Oeda and Kuto, 2018, Nonlinear Anal. RWA, 44, 589–615) obtained a bifurcation branch (connected set) of coexistence steady states which connects two semitrivial solutions. In Oeda and Kuto (2018, Nonlinear Anal. RWA, 44, 589–615), we also showed that any positive steady-state approaches a positive solution of either of two limiting systems, and moreover, one of the limiting systems is an equal diffusive competition model. This paper obtains the bifurcation structure of positive solutions to the other limiting system. Moreover, this paper implies that the global bifurcation branch of coexistence states consists of two parts, one of which is a simple curve running in a tubular domain near the set of positive solutions to the equal diffusive competition model, the other of which is a connected set characterized by positive solutions to the other limiting system.

scholarly journals Dynamic behavior analysis of a prey-predator model with ratio-dependent Monod-Haldane functional response

2018 ◽  
Vol 16 (1) ◽  
pp. 623-635 ◽  
Author(s):  
Xiaozhou Feng ◽  
Yi Song ◽  
Xiaomin An
Keyword(s):  
Fixed Point ◽  
Behavior Analysis ◽  
Dynamic Behavior ◽  
Fixed Point Index ◽  
Global Bifurcation ◽  
Index Theory ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Coexistence States ◽  
Predator Model

AbstractThis paper investigates the dynamic behavior analysis on the prey-predator model with ratio-dependent Monod-Haldane response function under the homogeneous Dirichlet boundary conditions, which is used to simulate a class of biological system. Firstly, the sufficient and necessary conditions on existence and non-existence of coexistence states of this model are discussed by comparison principle and fixed point index theory. Secondly, taking a as a main bifurcation parameter, the structure of global bifurcation curve on positive solutions is established by using global bifurcation theorem and properties of principal eigenvalue. Finally, the stability of coexistence states is obtained by the eigenvalue perturbation theory; the multiplicity of coexistence states is investigated when a satisfies some condition by the fixed point index theory.

scholarly journals Interventional radiology and artificial intelligence in radiology: Is it time to enhance the vision of our medical students?

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Pierre Auloge ◽  
Julien Garnon ◽  
Joey Marie Robinson ◽  
Sarah Dbouk ◽  
Jean Sibilia ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Interventional Radiology ◽  
Clinical Practice ◽  
Medical Students ◽  
Medical Curriculum ◽  
New Technology ◽  
Large Population ◽  
The Other ◽  
Clinical Phase ◽  
Preclinical Phase

Abstract Objectives To assess awareness and knowledge of Interventional Radiology (IR) in a large population of medical students in 2019. Methods An anonymous survey was distributed electronically to 9546 medical students from first to sixth year at three European medical schools. The survey contained 14 questions, including two general questions on diagnostic radiology (DR) and artificial intelligence (AI), and 11 on IR. Responses were analyzed for all students and compared between preclinical (PCs) (first to third year) and clinical phase (Cs) (fourth to sixth year) of medical school. Of 9546 students, 1459 students (15.3%) answered the survey. Results On DR questions, 34.8% answered that AI is a threat for radiologists (PCs: 246/725 (33.9%); Cs: 248/734 (36%)) and 91.1% thought that radiology has a future (PCs: 668/725 (92.1%); Cs: 657/734 (89.5%)). On IR questions, 80.8% (1179/1459) students had already heard of IR; 75.7% (1104/1459) stated that their knowledge of IR wasn’t as good as the other specialties and 80% would like more lectures on IR. Finally, 24.2% (353/1459) indicated an interest in a career in IR with a majority of women in preclinical phase, but this trend reverses in clinical phase. Conclusions Development of new technology supporting advances in artificial intelligence will likely continue to change the landscape of radiology; however, medical students remain confident in the need for specialty-trained human physicians in the future of radiology as a clinical practice. A large majority of medical students would like more information about IR in their medical curriculum; almost a quarter of students would be interested in a career in IR.

scholarly journals The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

2018 ◽  
Vol 26 (1) ◽  
pp. 5-41 ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Positive Solutions ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Global Bifurcation ◽  
Existence Of A Solution ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Global Bifurcation Theory ◽  
Necessary And Sufficient ◽  
Kirchhoff Type Problems

Abstract In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC SYSTEMS

1993 ◽  
Vol 03 (06) ◽  
pp. 823-837 ◽  
Author(s):  
A. CAÑADA ◽  
J.L. GÁMEZ
Keyword(s):  
Positive Solutions ◽  
Nonlinear Interaction ◽  
Spatial Dependence ◽  
Global Bifurcation ◽  
Elliptic Systems ◽  
Nonlinear Elliptic Systems ◽  
Decoupling Method ◽  
Nonlinear Elliptic ◽  
Cooperative Models

In this paper we prove the existence of nonnegative and non-trivial solutions of problems of the form [Formula: see text] Our main result improves many previous results of other authors and it may be applied to study the three standard situations: competition, prey-predator and cooperative models. We also cover some other cases which, due essentially to the spatial dependence or to a nonlinear interaction, are not any of these three types. The method of proof combines a decoupling method with a global bifurcation result.

scholarly journals A Lotka-Volterra Competition Model with Cross-Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Wenyan Chen ◽  
Ya Chen
Keyword(s):  
Boundary Condition ◽  
Positive Solutions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Cross Diffusion ◽  
Existence Of Positive Solutions

A Lotka-Volterra competition model with cross-diffusions under homogeneous Dirichlet boundary condition is considered, where cross-diffusions are included in such a way that the two species run away from each other because of the competition between them. Using the method of upper and lower solutions, sufficient conditions for the existence of positive solutions are provided when the cross-diffusions are sufficiently small. Furthermore, the investigation of nonexistence of positive solutions is also presented.

Coexistence states in a cross-diffusion system of a predator–prey model with predator satiation term

2018 ◽  
Vol 28 (11) ◽  
pp. 2131-2159 ◽  
Author(s):  
Willian Cintra ◽  
Cristian Morales-Rodrigo ◽  
Antonio Suárez
Keyword(s):  
A Priori ◽  
Diffusion System ◽  
Predator Satiation ◽  
Linear Diffusion ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Coexistence States ◽  
Predator Model

In this paper, we study the existence and non-existence of coexistence states for a cross-diffusion system arising from a prey–predator model with a predator satiation term. We use mainly bifurcation methods and a priori bounds to obtain our results. This leads us to study the coexistence region and compare our results with the classical linear diffusion predator–prey model. Our results suggest that when there is no abundance of prey, the predator needs to be a good hunter to survive.

A reaction-diffusion-advection competition model with a free boundary

2021 ◽  
Vol 65 (3) ◽  
pp. 25-37
Keyword(s):  
Free Boundary ◽  
A Priori Estimates ◽  
A Priori ◽  
Reaction Diffusion ◽  
Competition Model ◽  
Baseline Data ◽  
The Other ◽  
Quasilinear System ◽  
Priori Estimates ◽  
Competitive Diffusion

In this paper, we study a competitive diffusion quasilinear system with a free boundary. First, we investigate the mathematical questions of the problem. A priori estimates of Schauder type are established, which are necessary for the solvability of the problem. One of two competing species is an invader, which initially exists on a certain sub-interval. The other is initially distributed throughout the area under consideration. Examining the influence of baseline data on the success or failure of the first invasion. We conclude that there is a dichotomy of spread and extinction and give precise criteria for spread and extinction in this model.

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