Riccati-like flows and matrix approximations
Riccati's differential equation in birth-death processes.
This note reviews the occurrence of Riccati's equation in three birth-death type processes, and outlines their solutions.
Richardson Extrapolation combined with the sequential splitting procedure and the θ-method
Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.
Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point
Rings of constants of four-variable Lotka-Volterra systems
Lotka-Volterra systems appear in population biology, plasma physics, laser physics and derivation theory, among many others. We determine the rings of constants of four-variable Lotka-Volterra derivations with four parameters C 1, C 2, C 3, C 4 ∈ k, where k is a field of characteristic zero. Thus, we give a full description of polynomial first integrals of the respective systems of differential equations.
Rings of constants of generic 4D Lotka-Volterra systems
We show that the rings of constants of generic four-variable Lotka-Volterra derivations are finitely generated polynomial rings. We explicitly determine these rings, and we give a description of all polynomial first integrals of their corresponding systems of differential equations. Besides, we characterize cofactors of Darboux polynomials of arbitrary four-variable Lotka-Volterra systems. These cofactors are linear forms with coefficients in the set of nonnegative integers. Lotka-Volterra systems...
Robust dissipativity for uncertain impulsive dynamical systems.
Robust stabilization of fractional-order systems with interval uncertainties via fractional-order controllers.
Rosenbrock Methods for Differential Algebraic Equations.
Roughness of -dichotomies under small perturbations in .