New variational principles for locating periodic orbits of differential equations
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A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, E. Vanden-Eijnden, An ...
In this report we study and compare particular integration methods to solve ordinary differential equations, which are separable in solvable parts. The main source for this work is the article of Blanes and Casas: "On the necessity of negative coefficient ...
We track the secondary bifurcations of coherent states in plane Couette flow and show that they undergo a periodic doubling cascade that ends with a crisis bifurcation. We introduce a symbolic dynamics for the orbits and show that the ones that exist fall ...
The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation and the deactivation of inequality constraints ...
In this thesis we investigate different ways of approximating the solution of the chemical master equation (CME). The CME is a system of differential equations that models the stochastic transient behaviour of biochemical reaction networks. It does so by d ...
B-series are a fundamental tool in practical and theoretical aspects of numerical integrators for ordinary differential equations. A composition law for B-series permits an elegant derivation of order conditions, and a substitution law gives much insight i ...
We apply a new method for the determination of periodic orbits of general dynamical systems to the Lorenz equations. The accuracy of the expectation values obtained using this approach is shown to be much larger and have better convergence properties than ...
We present a new formulation for autonomous (i.e. time-independent) Dynamical Systems (DS) to perform discrete robot motions with em non-zero velocity at a given target. The proposed model ensures the convergence of all trajectories to the target, and is i ...
The 3DVAR filter is prototypical of methods used to combine observed data with a dynamical system, online, in order to improve estimation of the state of the system. Such methods are used for high dimensional data assimilation problems, such as those arisi ...
This paper presents a novel approach to real-time obstacle avoidance based on dynamical systems (DS) that ensures impenetrability of multiple convex shaped objects. The proposed method can be applied to perform obstacle avoidance in Cartesian and Joint spa ...