Search results for "Differential systems"
showing 7 items of 7 documents
Attraction in n ‐dimensional differential systems from network regulation theory
2018
Stability of impulsive differential systems
2013
The asymptotic phase property and reduction principle for stability of a trivial solution is generalized to the case of the noninvertible impulsive differential equations in Banach spaces whose linear parts split into two parts and satisfy the condition of separation.
Continuous numerical solutions of coupled mixed partial differential systems using Fer's factorization
1999
In this paper continuous numerical solutions expressed in terms of matrix exponentials are constructed to approximate time-dependent systems of the type ut A(t)uxx B(t)u=0; 0 0, u(0;t)=u(p;t)=0; u(x;0)=f(x);06 x6p. After truncation of an exact series solution, the numerical solution is constructed using Fer’s factorization. Given >0 and t0;t1; with 0<t0<t1 and D(t0;t1)=f(x;t); 06x6p; t06t6t1g the error of the approximated solution with respect to the exact series solution is less than uniformly in D(t0;t1). An algorithm is also included. c 1999 Elsevier Science B.V. All rights reserved. AMS classication: 65M15, 34A50, 35C10, 35A50
Two-Dimensional Differential Systems with Asymmetric Principal Part
2013
We consider the Sturm–Liouville nonlinear boundary value problem $$\displaystyle\begin{array}{rcl} \left \{\begin{array}{l} x^{\prime} = f(t,y) + u(t,x,y),\\ y^{\prime} = -g(t, x) + v(t, x, y), \end{array} \right.& & {}\\ \begin{array}{l} x(0)\cos \alpha - y(0)\sin \alpha = 0,\\ x(1)\cos \beta - y(1)\sin \beta = 0, \end{array} & & {}\\ \end{array}$$ assuming that the limits \(\lim _{y\rightarrow \pm \infty }\frac{f(t,y)} {y} = f_{\pm }\), \(\lim _{x\rightarrow \pm \infty }\frac{g(t,x)} {x} = g_{\pm }\) exist. Nonlinearities u and v are bounded. The system includes various cases of asymmetric equations (such as the Fucik one). Two classes of multiplicity results are discussed. The first one …
A Qualitative-Quantitative Approach to V-Belt Mechanics
1996
A simplified formulation is adopted for the theoretical problem of tension distribution and radial penetration of a V-belt along the pulley groove. The trajectory portrait of the second order differential system describing the belt behavior is carefully analyzed and asymptotic approximations for the tension solutions are derived which are well suited for design purposes.
Alcohol consumption in Spain and its economic cost: A mathematical modeling approach
2010
In this paper, a mathematical model for alcohol consumption in Spanish population is proposed. Its parameters are estimated by fitting the model to real data from Spanish Ministry of Health. Predictions about the future behavior of the alcohol consumption in Spain are presented using this model. Results are applied to estimate the economic costs (sanitary and non-sanitary) assumed by Spanish society that are derived from this consumption.
An upper bound of the index of an equilibrium point in the plane
2012
Abstract We give an upper bound of the index of an isolated equilibrium point of a C 1 vector field in the plane. The vector field is decomposed in gradient and Hamiltonian components. This decomposition is related with the Loewner vector field. Associated to this decomposition we consider the set Π where the gradient and Hamiltonian components are linearly dependent. The number of branches of Π starting at the equilibrium point determines the upper bound of the index.