Melnikov deviations and limit cycles for Lienard equations
Method of averaging for the system of functional-differential inclusions
The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form ⎧ (0) ⎨ ⎩ (1)
Methods of oscillation theory of half-linear second order differential equations
In this paper we investigate oscillatory properties of the second order half-linear equation Using the Riccati technique, the variational method and the reciprocity principle we establish new oscillation and nonoscillation criteria for (*). We also offer alternative methods of proofs of some recent oscillation results.
Minimal and maximal solutions of fourth order iterated differential equations with singular nonlinearity
In this paper we are concerned with sufficient conditions for the existence of minimal and maximal solutions of differential equations of the form where is the iterated linear differential operator of order and is a continuous function.
Model reduction methods for chaotic systems
Modeling Adaptive Behavior in Influenza Transmission
Contact behavior plays an important role in influenza transmission. In the progression of influenza spread, human population reduces mobility to decrease infection risks. In this paper, a mathematical model is proposed to include adaptive mobility. It is shown that the mobility response does not affect the basic reproduction number that characterizes the invasion threshold, but reduces dramatically infection peaks, or removes the peaks. Numerical...
Modeling schistosomiasis and HIV/AIDS codynamics.
Modeling the cytokine networkin vitro and in vivo.
Modeling the role of constant and time varying recycling delay on an ecological food chain
We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the...
Modélisation du champ de retard à la condensation d'un supraconducteur par un problème de bifurcation
Modelling the spiders ballooning effect on the vineyard ecology
We consider an ecosystem in which spiders may be transported by the wind from vineyards into the surrounding woods and vice versa. The model takes into account this tranport phenomenon without building space explicitly into the governing equations. The equilibria of the dynamical system are analyzed together with their stability, showing that bifurcations may occur. Then the effects of indiscriminated spraying to keep pests under control is also investigated via suitable simulations.
Modelling Tuberculosis and Hepatitis B Co-infections
Tuberculosis (TB) is the leading cause of death among individuals infected with the hepatitis B virus (HBV). The study of the joint dynamics of HBV and TB present formidable mathematical challenges due to the fact that the models of transmission are quite distinct. We formulate and analyze a deterministic mathematical model which incorporates of the co-dynamics of hepatitis B and tuberculosis. Two sub-models, namely: HBV-only and TB-only sub-models...
Models of interactions between heterotrophic and autotrophic organisms
We present two simple models describing relations between heterotrophic and autotrophic organisms in the land and water environments. The models are based on the Dawidowicz & Zalasiński models but we assume the boundedness of the oxygen resources. We perform a basic mathematical analysis of the models. The results of the analysis are complemented by numerical illustrations.
Models of learning and the polar decomposition of bounded linear operators.
Modifying some foliated dynamical systems to guide their trajectories to specified sub-manifolds
We show that dynamical systems in inverse problems are sometimes foliated if the embedding dimension is greater than the dimension of the manifold on which the system resides. Under this condition, we end up reaching different leaves of the foliation if we start from different initial conditions. For some of these cases we have found a method by which we can asymptotically guide the system to a specific leaf even if we start from an initial condition which corresponds to some other leaf. We demonstrate...
Monotone and Oscillatory Solutions of a Class of Nonlinear Differential Equations
Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions
The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.
Monotone methods applied to some higher order boundary value problems.
Monotone Methods for Periodic solutions of Second Order Scalar Functional Differential Equations.
Monotone solutions of a nonautonomous differential equation for a sedimenting sphere.