Melnikov analysis of chaos in a simple epidemiological model

被引：56

作者：

Glendinning, P ^{[1
]}

Perry, LP ^{[1
]}

机构：

[1] UNIV CAMBRIDGE, DEPT APPL MATH & THEORET PHYS, CAMBRIDGE CB3 9EW, ENGLAND

来源：

JOURNAL OF MATHEMATICAL BIOLOGY | 1997年 / 35卷 / 03期

关键词：

SIR models; chaos; Melnikov's method; homoclinic orbit;

D O I：

10.1007/s002850050056

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Melnikov's method is applied to an SIR model of epidemic dynamics with a periodically modulated nonlinear incidence rate. This analysis establishes mathematically, for the first time, the existence of chaotic motion in these models. A related technique also makes it possible to prove that homoclinic bifurcations occurs in the model.

引用

页码：359 / 373

页数：15

共 21 条

[1]

ANDERSON R M, 1991

[2] SEASONALITY AND PERIOD-DOUBLING BIFURCATIONS IN AN EPIDEMIC MODEL [J].

ARON, JL ;

SCHWARTZ, IB .

JOURNAL OF THEORETICAL BIOLOGY, 1984, 110 (04) :665-679

[3] COMPLEX BIFURCATIONS IN A PERIODICALLY FORCED NORMAL-FORM [J].

BAESENS, C ;

NICOLIS, G .

ZEITSCHRIFT FUR PHYSIK B-CONDENSED MATTER, 1983, 52 (04) :345-354

[4]

Chow S. -N., 1994, NORMAL FORMS BIFURCA

[5] DOES FACILITATION IMPLY A THRESHOLD FOR THE ERADICATION OF LYMPHATIC FILARIASIS [J].

DYE, C .

PARASITOLOGY TODAY, 1992, 8 (04) :109-110

[6] HOMOCLINIC ORBITS AND MIXED-MODE OSCILLATIONS IN FAR-FROM-EQUILIBRIUM SYSTEMS [J].

GASPARD, P ;

WANG, XJ .

JOURNAL OF STATISTICAL PHYSICS, 1987, 48 (1-2) :151-199

[7]

Gavrilov N. K., 1973, Mat. Sb. (N.S.), V90, P139

[8]

Gavrilov NK, 1972, MATH USSR SB, V17, P467, DOI [10.1070/sm1972v017n04abeh001597, DOI 10.1070/SM1972V017N04ABEH001597]

[9]

Guckenheimer J., 2013, NONLINEAR OSCILLATIO, V42, DOI DOI 10.1007/978-1-4612-1140-2

[10] SOME EPIDEMIOLOGIC MODELS WITH NONLINEAR INCIDENCE [J].

HETHCOTE, HW ;

VANDENDRIESSCHE, P .

JOURNAL OF MATHEMATICAL BIOLOGY, 1991, 29 (03) :271-287

← 1 2 3 →