Spreading speed of the periodic Lotka-Volterra competition model

2021 ◽  
Vol 275 ◽  
pp. 533-553
Author(s):  
Xiaolin Liu ◽  
Zigen Ouyang ◽  
Zhe Huang ◽  
Chunhua Ou
Keyword(s):  
Competition Model ◽  
Spreading Speed

Estimation of receptor occupancy and synaptic dopamine after amphetamine challenge: A competition model approach

2005 ◽  
Vol 25 (1_suppl) ◽  
pp. S613-S613
Author(s):  
Hiroto Kuwabara ◽  
Anil Kumar ◽  
James Brasic ◽  
Ayon Nandi ◽  
Dean F Wong
Keyword(s):  
Receptor Occupancy ◽  
Competition Model ◽  
Model Approach

scholarly journals Optimal solution of the fractional order breast cancer competition model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Hassani ◽  
J. A. Tenreiro Machado ◽  
Z. Avazzadeh ◽  
E. Safari ◽  
S. Mehrabi
Keyword(s):  
Breast Cancer ◽  
Fractional Order ◽  
Legendre Polynomials ◽  
Numerical Experiments ◽  
Optimal Solution ◽  
Optimization Method ◽  
Competition Model ◽  
Basis Functions ◽  
Cell Populations ◽  
Operational Matrices

AbstractIn this article, a fractional order breast cancer competition model (F-BCCM) under the Caputo fractional derivative is analyzed. A new set of basis functions, namely the generalized shifted Legendre polynomials, is proposed to deal with the solutions of F-BCCM. The F-BCCM describes the dynamics involving a variety of cancer factors, such as the stem, tumor and healthy cells, as well as the effects of excess estrogen and the body’s natural immune response on the cell populations. After combining the operational matrices with the Lagrange multipliers technique we obtain an optimization method for solving the F-BCCM whose convergence is investigated. Several examples show that a few number of basis functions lead to the satisfactory results. In fact, numerical experiments not only confirm the accuracy but also the practicability and computational efficiency of the devised technique.

More evidence on competing cognitive systems

1985 ◽  
Vol 1 (1) ◽  
pp. 47-72 ◽  
Author(s):  
Sascha W. Felix
Keyword(s):  
Second Language ◽  
Problem Solving ◽  
General Problem ◽  
Learning Process ◽  
Native Speaker ◽  
Universal Grammar ◽  
Learning Task ◽  
Competition Model ◽  
Cognitive Systems ◽  
Specific System

This paper deals with the question of why adults, as a rule, fail to achieve native-speaker competence in a second language, whereas children appear to be generally able to acquire full command of either a first or second language. The Competition Model proposed in this paper accounts for this difference in terms of different cognitive systems or modules operating in child and adult language acquisition. It is argued that the child's learning process is guided by a language-specific module, roughly equivalent to Universal Grammar (cf. Chomsky, 1980), while adults tend to approach the learning task by utilizing a general problem-solving module which enters into competition with the language-specific system. The crucial evidence in support of the Competition Model comes from a) the availability of formal operations in different modules and b) from differences in the types of utterances produced by children and adults.

An evolutional free-boundary problem of a reaction–diffusion–advection system

2017 ◽  
Vol 147 (3) ◽  
pp. 615-648 ◽  
Author(s):  
Ling Zhou ◽  
Shan Zhang ◽  
Zuhan Liu
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Ecological Model ◽  
Reaction Diffusion ◽  
Spreading Speed ◽  
Heterogeneous Environment ◽  
Long Run ◽  
Strong Competition ◽  
Asymptotic Spreading

In this paper we consider a system of reaction–diffusion–advection equations with a free boundary, which arises in a competition ecological model in heterogeneous environment. The evolution of the free-boundary problem is discussed, which is an extension of the results of Du and Lin (Discrete Contin. Dynam. Syst. B19 (2014), 3105–3132). Precisely, when u is an inferior competitor, we prove that (u, v) → (0, V) as t→∞. When u is a superior competitor, we prove that a spreading–vanishing dichotomy holds, namely, as t→∞, either h(t)→∞ and (u, v) → (U, 0), or limt→∞h(t) < ∞ and (u, v) → (0, V). Moreover, in a weak competition case, we prove that two competing species coexist in the long run, while in a strong competition case, two species spatially segregate as the competition rates become large. Furthermore, when spreading occurs, we obtain some rough estimates of the asymptotic spreading speed.

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