Instability and complex dynamic behaviour in population models with long time delays

1982 ◽  
Vol 22 (2) ◽  
pp. 147-176 ◽  
Author(s):  
S.P. Blythe ◽  
R.M. Nisbet ◽  
W.S.C. Gurney
1976 ◽  
Vol 12 (22) ◽  
pp. 574 ◽  
Author(s):  
F.D. Nunes ◽  
N.B. Patel ◽  
J.E. Ripper
Keyword(s):  

2007 ◽  
Vol 4 (16) ◽  
pp. 841-849 ◽  
Author(s):  
Maite Severins ◽  
Don Klinkenberg ◽  
Hans Heesterbeek

Infection systems where traits of the host, such as acquired immunity, interact with the infection process can show complex dynamic behaviour with counter-intuitive results. In this study, we consider the traits ‘immune status’ and ‘exposure history’, and our aim is to assess the influence of acquired individual heterogeneity in these traits. We have built an individual-based model of Eimeria acervulina infections, a protozoan parasite with an environmental stage that causes coccidiosis in chickens. With the model, we simulate outbreaks of the disease under varying initial contaminations. Heterogeneity in the traits arises stochastically through differences in the dose and frequency of parasites that individuals pick up from the environment. We find that the relationship between the initial contamination and the severity of an outbreak has a non-monotonous ‘wave-like’ pattern. This pattern can be explained by an increased heterogeneity in the host population caused by the infection process at the most severe outbreaks. We conclude that when dealing with these types of infection systems, models that are used to develop or evaluate control measures cannot neglect acquired heterogeneity in the host population traits that interact with the infection process.


2015 ◽  
Vol 105 (05) ◽  
pp. 263-268
Author(s):  
P. H. Nebeling

Das dynamische Verhalten von Werkzeugmaschinen ist für die Stabilität während der Bearbeitung sowie die Qualität der erzeugten Werkstücke von besonderer Bedeutung. Ein Einflussfaktor darauf ist die Dämpfung. Im Bereich der Maschinengestelle kommen seit langer Zeit unterschiedliche Materialien zum Einsatz. In diesem Fachbeitrag werden die Dämpfungskennwerte unterschiedlicher Gestellwerkstoffe an geometrisch gleichen Proben vergleichend gegenübergestellt. Als weitere Kenngröße wurde die Lage der (1. Biege-) Eigenfrequenz als Maß für die massebezogene dynamische Steifigkeit verwendet. Die Effekte beim Übergang von einfachen Bauteilen zu komplexen Strukturen runden den Fachartikel ab.   The dynamic behaviour of machine tools is of great importance for stability and quality of the machined work pieces. One influencing factor in this area is damping. In the field of machine bases different materials have been use since long time. In this article the damping values of different materials with equal geometric properties are compared. As further parameter the first bending Eigenfrequency as dimension for mass related stiffness is use. The transition from simple components to complex structures is touched at the end of the paper.


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