Dynamics and Patterns of a Diffusive Prey-Predator System with a Group Defense for Prey

We study a diffusive prey-predator system with a group defense for prey. Under Neumann boundary condition, we analyze local and stability of nonnegative constant steady states and the existence and nonexistence of nonconstant steady states. These results also exhibit the critical role of the system parameters leading to the formation of spatiotemporal patterns.

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Positive steady states of the Holling–Tanner prey–predator model with diffusion

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500003814 ◽

2005 ◽

Vol 135 (1) ◽

pp. 149-164 ◽

Cited By ~ 66

Author(s):

Rui Peng ◽

Mingxin Wang

Keyword(s):

Boundary Condition ◽

Neumann Boundary Condition ◽

Neumann Boundary ◽

Steady States ◽

Homogeneous Neumann Boundary Condition ◽

Positive Steady States ◽

Predator Model

This paper is concerned with the Holling–Tanner prey–predator model with diffusion subject to the homogeneous Neumann boundary condition. We obtain the existence and non-existence of positive non-constant steady states.

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Bifurcations and Multistability in a Model of Cytokine-Mediated Autoimmunity

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419500342 ◽

2019 ◽

Vol 29 (03) ◽

pp. 1950034 ◽

Cited By ~ 1

Author(s):

Farzad Fatehi ◽

Yuliya N. Kyrychko ◽

Robert Molchanov ◽

Konstantin B. Blyuss

Keyword(s):

T Cells ◽

Chronic Infection ◽

Initial Conditions ◽

Cell Activity ◽

Basins Of Attraction ◽

Activity Analysis ◽

Steady States ◽

System Parameters ◽

Stability And Bifurcations

This paper investigates the dynamics of immune response and autoimmunity with particular emphasis on the role of regulatory T cells (Tregs), T cells with different activation thresholds, and cytokines in mediating T cell activity. Analysis of the steady states yields parameter regions corresponding to regimes of normal clearance of viral infection, chronic infection, or autoimmune behavior, and the boundaries of stability and bifurcations of relevant steady states are found in terms of system parameters. Numerical simulations are performed to illustrate different dynamical scenarios, and to identify basins of attraction of different steady states and periodic solutions, highlighting the important role played by the initial conditions in determining the outcome of immune interactions.

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Critical role of Prandtl number on multiple steady states during natural convection in square enclosures: Analysis of heat transfer rates, flow and thermal maps

International Journal of Heat and Mass Transfer ◽

10.1016/j.ijheatmasstransfer.2021.120900 ◽

2021 ◽

Vol 170 ◽

pp. 120900

Author(s):

Madhuchhanda Bhattacharya ◽

Tanmay Basak

Keyword(s):

Heat Transfer ◽

Natural Convection ◽

Prandtl Number ◽

Critical Role ◽

Steady States ◽

Multiple Steady States ◽

Transfer Rates

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is known. is a known term with A role of the Neumann boundary condition for

Hydraulic Engineering Software IV ◽

10.1201/9781482286809-67 ◽

2003 ◽

pp. 192-192

Keyword(s):

Boundary Condition ◽

Neumann Boundary Condition ◽

Neumann Boundary

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The Role of the SLP in Autism Spectrum Disorder Screening and Assessment

Perspectives on Language Learning and Education ◽

10.1044/lle15.2.50 ◽

2008 ◽

Vol 15 (2) ◽

pp. 50-59 ◽

Cited By ~ 1

Author(s):

Amy Philofsky

Keyword(s):

Language Development ◽

Critical Role ◽

Children With Autism ◽

Autism Spectrum ◽

Children With Asd ◽

Prevalence Estimates ◽

Notable Increase ◽

Screening Assessment ◽

Critical Components

AbstractRecent prevalence estimates for autism have been alarming as a function of the notable increase. Speech-language pathologists play a critical role in screening, assessment and intervention for children with autism. This article reviews signs that may be indicative of autism at different stages of language development, and discusses the importance of several psychometric properties—sensitivity and specificity—in utilizing screening measures for children with autism. Critical components of assessment for children with autism are reviewed. This article concludes with examples of intervention targets for children with ASD at various levels of language development.

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