Global existence and asymptotic behavior of solution of second-order nonlinear impulsive differential equations.
Global stability of steady solutions for a model in virus dynamics
We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...
Global Stability of Steady Solutions for a Model in Virus Dynamics
We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...
Globally convergent differential procedures for solving nonlinear systems of equations
Growth estimates for non-oscillatory solutions of a non-linear differential equation
Half-explicit Runge-Kutta methods for semi-explicit differential-algebraic equations of index 1.
Herbivore harvesting and alternative steady states in coral reefs
Coral reefs can undergo relatively rapid changes in the dominant biota, a phenomenon referred to as phase shift. Degradation of coral reefs is often associated with changes in community structure towards a macroalgae-dominated reef ecosystem due to the reduction in herbivory caused by overfishing. We investigate the coral-macroalgal phase shift due to the effects of harvesting of herbivorous reef fish by means of a continuous time model in the food chain. Conditions for local asymptotic stability...
He's variational iteration method for solving fractional Riccati differential equation.
High order explicit Runge-Kutta pairs for ephemerides of the solar system and the Moon.
Higher-index differential-algebraic equations: analysis and numerical treatment
How to Increase the Order to Get Minimal-Error Algorithms for Systems of ODE.
Implicit Runge-Kutta methods for transferable differential-algebraic equations
The numerical solution of transferable differential-algebraic equations (DAE’s) by implicit Runge-Kutta methods (IRK) is studied. If the matrix of coefficients of an IRK is non-singular then the arising systems of nonlinear equations are uniquely solvable. These methods are proved to be stable if an additional contractivity condition is satisfied. For transferable DAE’s with smooth solution we get convergence of order , where is the classical order of the IRK and is the stage order. For transferable...
Importance of brood maintenance terms in simple models of the honeybee - Varroa destructor - acute bee paralysis virus complex.
Increasing solutions of Thomas-Fermi type differential equations - the sublinear case
Input-output systems in Biology and Chemistry and a class of mathematical models describing them
Our aim is to show a class of mathematical models in application to some problems of cell biology. Typically, our models are described via classical chemical networks. This property is visualized by a conservation law. Mathematically, this conservation law guarantees most of the mathematical properties of the models such as global existence and uniqueness of solutions as well as positivity of the solutions for positive data. These properties are consequences of the fact that the infinitesimal generators...
Instability of solutions of certain nonlinear vector differential equations of third order.
Integral equivalence between a nonlinear system and its nonlinear perturbation
Integral Equivalence of Two Systems of Differential Equations
Si studia l'equivalenza asintotica fra le soluzioni di un sistema lineare e quelle di una perturbazione non lineare. Vengono date condizioni sufficienti per l'esistenza di un omeomorfìsmo fra le soluzioni limitate di tali sistemi.
Invariant foliations and stability in critical cases.
Invariant manifolds of a differentiable vector field