shift in Hopf bifurcations for a class of nonstandard numerical schemes.
A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems.
Bifurcation analysis of the Hénon map.
Computation and continuation of quasiperiodic solutions
Higher period stochastic bifurcation of nonlinear airfoil fluid-structure interaction.
Linear bifurcation analysis with applications to relative socio-spatial dynamics.
Numerical bifurcation of separable parameterized equations.
One-Parameter Bifurcation Analysis of Dynamical Systems using Maple
This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.* This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–359/2008.
Parametrically excited nonlinear systems: A comparison of two methods.
Reminiscences on science at IHÉS. A problem on homoclinic theory and a brief review
Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems
We propose a new rigorous numerical technique to prove the existence of symmetric homoclinic orbits in reversible dynamical systems. The essential idea is to calculate Melnikov functions by the exponential dichotomy and the rigorous numerics. The algorithm of our method is explained in detail by dividing into four steps. An application to a two dimensional reversible system is also treated and the existence of a symmetric homoclinic orbit is rigorously verified as an example.
Stability and bifurcation of numerical discretization Nicholson blowflies equation with delay.