Homoclinic Bifurcation in an SIQR Model for Childhood Diseases
نویسندگان
چکیده
We consider a system of ODEs which describes the transmission dynamics of childhood diseases. A center manifold reduction at a bifurcation point has the normal form x$= y, y$=axy+bxy+O(4), indicating a bifurcation of codimension greater than two. A three-parameter unfolding of the normal form is studied to capture possible complex dynamics of the original system which is subjected to certain constraints on the state space due to biological considerations. It is shown that the perturbed system produces homoclinic bifurcation. 2000 Academic Press
منابع مشابه
An SEIQR model for childhood diseases.
It has been shown that the inclusion of an isolated class in the classical SIR model for childhood diseases can be responsible for self-sustained oscillations. Hence, the recurrent outbreaks of such diseases can be caused by autonomous, deterministic factors. We extend the model to include a latent class (i.e. individuals who are infected with the disease, but are not yet able to pass the disea...
متن کاملHomoclinic Bifurcations in Reversible Systems
The thesis investigates bifurcations from homoclinic solutions of ordinary differential equations. Homoclinic solutions are characterised by approaching an equilibrium, i.e. a constant solution of a differential equation, in both positive and negative time. The thesis is devoted to the analysis of homoclinic bifurcations that originate from a change in the type of the associated equilibrium. Se...
متن کاملA Numerical Bifurcation Function for Homoclinic Orbits
We present a numerical method to locate periodic orbits near homoclinic orbits. Using a method of X.-B. Lin and solutions of the adjoint variational equation, we get a bifurcation function for periodic orbits whose period is asymptotic to innnity on approaching a homoclinic orbit. As a bonus, a linear predictor for continuation of the homoclinic orbit is easily available. Numerical approximatio...
متن کاملBifurcation of a Modified BVP Circuit Model for Neurons Generating Rectangular Waves
We investigate bifurcations of burst oscillations with rectangular waveform observed in a modified Bonhöffer-van der Pol equation, which is considered as a circuit model for neurons of a feeding rhythm generator. In particular, we clarify a mechanism of properties in a one-parameter graph on the period of oscillations, showing a staircase with hysteresis jumps, by studying a successive bifurcat...
متن کاملSaddle Invariant Objects and Their Global Manifolds in a Neighborhood of a Homoclinic Flip Bifurcation of Case B
When a real saddle equilibrium in a three-dimensional vector field undergoes a homoclinic bifurcation, the associated two-dimensional invariant manifold of the equilibrium closes on itself in an orientable or non-orientable way, provided the corresponding genericity conditions. We are interested in the interaction between global invariant manifolds of saddle equilibria and saddle periodic orbit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000