On a codimension two bifurcation for a class of second order ODEs
ثبت نشده
چکیده
منابع مشابه
On second derivative 3-stage Hermite--Birkhoff--Obrechkoff methods for stiff ODEs: A-stable up to order 10 with variable stepsize
Variable-step (VS) second derivative $k$-step $3$-stage Hermite--Birkhoff--Obrechkoff (HBO) methods of order $p=(k+3)$, denoted by HBO$(p)$ are constructed as a combination of linear $k$-step methods of order $(p-2)$ and a second derivative two-step diagonally implicit $3$-stage Hermite--Birkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for co...
متن کاملBifurcation Analysis of a Prey-Predator Coevolution Model
We show in this paper how numerical bifurcation analysis can be used to study the evolution of genetically transmitted phenotypic traits. For this, we consider the standard Rosenzweig-MacArthur prey-predator model and, following the so-called Adaptive Dynamics approach, we derive from it a second-order evolutionary model composed of two ODEs, one for the prey trait and one for the predator trai...
متن کاملHomoclinic Bifurcation in an SIQR Model for Childhood Diseases
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 co...
متن کاملCodimension-Two Bifurcations of Fixed Points in a Class of Discrete Prey-Predator Systems
The dynamic behaviour of a Lotka-Volterra system, described by a planar map, is analytically and numerically investigated. We derive analytical conditions for stability and bifurcation of the fixed points of the system and compute analytically the normal form coefficients for the codimension 1 bifurcation points flip and Neimark-Sacker , and so establish subor supercriticality of these bifurcat...
متن کاملInstabilities induced by a weak breaking of a strong spatial resonance
Through multiple-scales and symmetry arguments we derive a model set of amplitude equations describing the interaction of two steady-state pattern-forming instabilities, in the case that the wavelengths of the instabilities are nearly in the ratio 1 : 2. In the case of exact 1 : 2 resonance the amplitude equations are ODEs; here they are PDEs. We discuss the stability of spatially-periodic solu...
متن کامل