An analysis of the complex dynamic behaviour of nonlinear oligopoly models with time delays

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.

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On the complex dynamic behaviour in nonlinear systems with delay

Chaos Solitons & Fractals ◽

10.1016/0960-0779(95)80014-8 ◽

1995 ◽

Vol 6 ◽

pp. 83-87 ◽

Cited By ~ 1

Author(s):

H.G. Chiacchiarini ◽

J.L. Moiola ◽

A.C. Desages

Keyword(s):

Nonlinear Systems ◽

Dynamic Behaviour ◽

Complex Dynamic

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Selection between multiple periodic regimes in a biochemical system: Complex dynamic behaviour resolved by use of one-dimensional maps

Journal of Theoretical Biology ◽

10.1016/s0022-5193(85)80185-5 ◽

1985 ◽

Vol 113 (4) ◽

pp. 649-671 ◽

Cited By ~ 15

Author(s):

O. Decroly ◽

A. Goldbeter

Keyword(s):

Dynamic Behaviour ◽

Complex Dynamic ◽

Biochemical System ◽

One Dimensional ◽

One Dimensional Maps

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Analysis of an aerodynamic grooved journal bearing with plain sleeve

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/095440605x69462 ◽

2006 ◽

Vol 220 (1) ◽

pp. 51-60 ◽

Cited By ~ 1

Author(s):

C-C Wang

Keyword(s):

Reynolds Equation ◽

Dynamic Behaviour ◽

Journal Bearing ◽

Power Spectra ◽

Operating Conditions ◽

Complex Dynamic ◽

Non Linear ◽

Linear Behaviour ◽

Bearing Number ◽

Rotor Mass

This article studies the non-linear behaviour of a herringbone-grooved rigid rotor supported by a gas film bearing. A numerical method is employed to a time-dependent mathematical model for herringbone-grooved gas journal bearings. The finite difference method with successive over-relation method is employed to solve the Reynolds equation. The system state trajectory, Poincaré maps, power spectra, and bifurcation diagrams are used to analyse the dynamic behaviour of the rotor centre in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behaviour comprising periodic and quasi-periodic responses of the rotor centre. This article shows how the dynamic behaviour of this type of system varies with changes in rotor mass and bearing number. The results of this study contribute to a further understanding of the non-linear dynamics of aerodynamic-grooved journal bearing systems.

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Analysis of the Effect of Coulomb Friction on Haptic Systems Dynamics

Volume 6: 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2016-59961 ◽

2016 ◽

Author(s):

Csaba Budai ◽

László L. Kovács ◽

József Kövecses

Keyword(s):

Coulomb Friction ◽

Dynamic Behaviour ◽

Systems Dynamics ◽

Data Systems ◽

Sampled Data ◽

Complex Dynamic ◽

System Parameters ◽

Human Machine Interfaces ◽

And Performance ◽

Experiment Analysis

Dissipation mechanisms and dissipative forces play a pivotal role in the operations and performance of human-machine interfaces and particularly in haptic systems. Dissipation is a very difficult phenomenon to model. Coulomb friction in general can be the most influential element in systems involving multiple direct contact connections such as joints with transmissions or mechanically guided components. Coulomb friction includes non-smooth discontinuity and can induce complex dynamic behaviours. Very little attention has been paid to the analysis of the effects of Coulomb friction in haptic devices. In this paper we illustrate, by experiment, analysis and simulation, the nature of the dynamic behaviour caused by Coulomb friction in haptic sampled-data systems. We demonstrate that a simple model can represent this behaviour, and show the effects of the haptic system parameters on this dynamics.

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