Bifurcations of equilibria of a non-linear age structured model

M. E. Gurtin and R. C. MacCamy investigated a non-linear age-structured population dynamical model, which served as one of the basic non-linear population dynamical models in the last three decades. They described a characteristic equation but they did not use it to discuss stability of equilibria of the system in certain special cases. In a recent paper, M. Farkas deduced a characteristic equation in another form. This characteristic equation enabled us to prove results about the stability of stationary age distributions of the system. In the present paper we are going to investigate how equilibria arise and change their stability as a basic parameter of the system varies

Net reproduction functions for nonlinear structured population models

The goal of this note is to present a general approach to define the net reproduction function for a large class of nonlinear physiologically structured population models. In particular, we are going to show that this can be achieved in a natural way by reformulating a nonlinear problem as a family of linear ones; each of the linear problems describing the evolution of the population in a different, but constant environment. The reformulation of a nonlinear population model as a family of linear ones is a new approach, and provides an elegant way to study qualitative questions, for example the existence of positive steady states. To define the net reproduction number for any fixed (constant) environment, i.e. for the linear models, we use a fairly recent spectral theoretic result, which characterizes the connection between the spectral bound of an unbounded operator and the spectral radius of a corresponding bounded operator. For nonlinear models, varying the environment naturally leads to a net reproduction function

Structured populations: The stabilizing effect of the inflow of newborns from an external source and the net growth rate

We investigate the effect of a positive population inflow of individuals from an external source on the dynamical behaviour of certain physisologically structured population models. We treat a size-structured model with constant inflow and nonlinear birth rate and an age-structured model with nonlinear (density dependent) inflow and linear birth rate. Analogously to the inherent net reproduction rate we introduce a net growth rate and discuss how this net growth rate can be related to our stability/instability conditions

Dynamics of Perceptual Organization in Complex Visual Search: The Identification of Self Organized Criticality with Respect to Visual Grouping Principles

The current project applies modern quantitative theories of visual perception to examine the effect of the Gestalt Law of proximity on visual cognition. Gestalt Laws are spontaneous dynamic processes (Brunswik & Kamiya, 1953; Wertheimer, 1938) that underlie the principles of perceptual organization. These principles serve as mental short-cuts, heuristic rule-of-thumb strategies that shorten decision-making time and allow continuous, efficient processing and flow of information (Hertwig & Todd, 2002). The proximity heuristic refers to the observation that objects near each other in the visual field tend to be grouped together by the perceptual system (Smith-Gratto & Fisher, 1999). Proximity can be directly quantified as the distance between adjacent objects (inter-object distances) in a visual array. Recent studies on eye movements have revealed the interactive nature of self organizing dynamic processes in visual cognition (Aks, Zelinsky, & Sprott, 2002; Stephen, & Mirman, 2010). Research by Aks and colleagues (2002) recorded eye-movements during a complex visual search task in which participants searched for a target among distracters. Their key finding was that visual search patterns are not randomly distributed, and that a simple form of temporal memory exists across the sequence of eye movements. The objective of the present research was to identify how the law of proximity impacts visual search behavior as reflected in eye movement patterns. We discovered that 1) eye movements are fractal; 2) more fractality will result in decreased reaction time during visual search, and 3) fractality facilitates the improvement of reaction times over blocks of trials. Results were interpreted in view of theories of cognitive resource allocation and perceptual efficiency. The current research could inspire potential innovations in computer vision, user interface design and visual cognition

Stability conditions for a non-linear size-structured model

In this paper we consider a general non-linear size-structured population dynamical model with size- and density-dependent fertility and mortality rates and with size-dependent growth rate. Based on M. Farkas (Appl. Math. Comput. 131 (1) (2002) 107-123) we are able to deduce a characteristic function for a stationary solution of the system in a similar way. Then we establish results about the stability (resp. instability) of the stationary solutions of the system

Developments in Hungary in Staffing Practices - Results of Two Consecutive Cranet Surveys

Management of human resources, the same as other fields of management, has altered significantly in Hungary since the democratic transformation and in many respects it is still changing. This paper – while describing the specific Hungarian staffing practice and its alterations – makes a comparison of the characteristics of the Hungarian samples of two Cranet surveys. Based on these, we outline the ratio of similarity between the Hungarian and the global (or that of the 32 countries participating in the network) HR practice and the features of HR practices of (6 network member) countries from the Central and Eastern European (CEE) region.Human Resource Management, staffing, Hungary, Cranet

Asymptotic behavior of size-structured populations via juvenile-adult interaction

In this work a size structured juvenile-adult population model is considered. The linearized dynamical behavior of stationary solutions is analyzed using semigroup and spectral methods. The regularity of the governing linear semigroup allows to derive biologically meaningful conditions for the linear stability of stationary solutions. The main emphasis in this work is on juvenile-adult interaction and resulting consequences for the dynamics of the system. In addition, we investigate numerically the effect of a non-zero population inflow, due to an external source of newborns, on the dynamical behavior of the system in a special case of model ingredients

On a strain-structured epidemic model

We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the interesting scenario when individuals infected with different strains cause secondary (new) infections at different rates. Therefore, we consider a nonlinear infection process, which generalises the bilinear process arising from the classic mass-action assumption. Our main motivation is to study competition between different strains of a virus/bacteria. From the mathematical point of view, we are interested whether the nonlinear infection process leads to a well-posed model. We use a semilinear formulation to show global existence and positivity of solutions up to a critical value of the exponent in the nonlinearity. Furthermore, we establish the existence of the endemic steady state for particular classes of nonlinearities