A piece wise linear suspension bridge model: nonlinear dynamics and orbit continuation

Doole, SH; Hogan, S. J.

doi:10.1080/02681119608806215

Cited by 69 publications

(35 citation statements)

References 34 publications

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“…E In a similar way the oscillations of suspension bridges may be in#uenced by variable sti!ness with very fast variations since the suspension cables are much sti!er in tension than in compression [2]. E The dynamics of systems idealized by a block with non-smooth surface excited on a #at plate is hugely in#uenced by the properties of the transition between di!erent portions of the contact surface [3].…”

Section: Introductionmentioning

confidence: 98%

Some Discontinuous Bifurcations in a Two-Block Stick–slip System

Galvanetto

2001

Journal of Sound and Vibration

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Section: Introductionmentioning

confidence: 98%

Some Discontinuous Bifurcations in a Two-Block Stick–slip System

Galvanetto

2001

Journal of Sound and Vibration

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“…In this case the models (1.2) and (1.3) can be rewritten as a Filippov system, a model which has been applied widely in many fields of science and engineering. Furthermore, the theory of Filippov systems is being recognized as not only richer than the corresponding theory of continuous systems, but also as representing a more natural framework for the mathematical modelling of real-world phenomena [18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Ag(t)(c + Mi(t)/(n + I(t))mentioning

confidence: 99%

Modelling the regulatory system for diabetes mellitus with a threshold window

Tang

Cheke

2015

Communications in Nonlinear Science and Numerical Simulation

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Please cite this article as: Yang, J., Tang, S., Cheke, R.A., Modelling the regulatory system for diabetes mellitus with a threshold window, Communications in Nonlinear Science and Numerical Simulation (2014), doi: http:// dx.doi.org/10.1016/j.cnsns. 2014.08.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Modelling the regulatory system for diabetes mellitus with a threshold window AbstractPiecewise (or non-smooth) glucose-insulin models with threshold windows for type 1 and type 2 diabetes mellitus are proposed and analyzed with a view to improving understanding of the glucose-insulin regulatory system. For glucose-insulin models with a single threshold, the existence and stability of regular, virtual, pseudo-equilibria and tangent points are addressed. Then the relations between regular equilibria and a pseudo-equilibrium are studied. Furthermore, the sufficient and necessary conditions for the global stability of regular equilibria and the pseudo-equilibrium are provided by using qualitative analysis techniques of non-smooth Filippov dynamic systems. Sliding bifurcations related to boundary node bifurcations were investigated with theoretical and numerical techniques, and insulin clinical therapies are discussed. For glucose-insulin models with a threshold window, the effects of glucose thresholds or the widths of threshold windows on the durations of insulin therapy and glucose infusion were addressed. The duration of the effects of an insulin injection is sensitive to the variation of thresholds. Our results indicate that blood glucose level can be maintained within a normal range using piecewise glucose-insulin models with a single threshold or a threshold window. Moreover, our findings suggest that it is critical to individualize insulin therapy for each patient separately, based on initial blood glucose levels.

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“…In [11][12][13], Equation (4) has been studied numerically by using either continuation methods or variational numerical methods in order to gain more information on the structure of the equation solutions set. In [14] Humphreys and McKenna considered the existence of multiple periodic solutions for the nonlinear beam Equation (4), while in [15,16] Doole and Hogan transformed the beam Equation (4) into an ordinary differential equation and treated it by using dynamical systems method. Recently, there are also some researches devoted to symmetry group structure and exact solutions of the fourth-order nonlinear beam Equation (4) [17,18].…”

Section: Introductionmentioning

confidence: 99%

Lie Symmetry Classification of the Generalized Nonlinear Beam Equation

Huang

2017

Symmetry

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Abstract:In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation with both second-order and fourth-order wave terms, which is extended from the classical beam equation arising in the historical events of travelling wave behavior in the Golden Gate Bridge in San Francisco. We perform a complete Lie symmetry group classification by using the equivalence transformation group theory for the equation under consideration. Lie symmetry reductions of a nonlinear beam-like equation which are singled out from the classification results are investigated. Some classes of exact solutions, including solitary wave solutions, triangular periodic wave solutions and rational solutions of the nonlinear beam-like equations are constructed by means of the reductions and symbolic computation.

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A piece wise linear suspension bridge model: nonlinear dynamics and orbit continuation

Cited by 69 publications

References 34 publications

Some Discontinuous Bifurcations in a Two-Block Stick–slip System

Some Discontinuous Bifurcations in a Two-Block Stick–slip System

Modelling the regulatory system for diabetes mellitus with a threshold window

Lie Symmetry Classification of the Generalized Nonlinear Beam Equation

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