The unsteady (nonautonomous) analog of a hyperbolic fixed point is a hyperbolic trajectory, whose importance is underscored by its attached stable and unstable manifolds, which have relevance in fluid flow barriers, chaotic basin boundaries, and the long-term behavior of the system. We develop a method for obtaining the unsteady control velocity which forces a hyperbolic trajectory to follow a ...

Long terminal repeat (LTR) retrotransposons, the most abundant genomic components in flowering plants, are classifiable into autonomous and nonautonomous elements based on their structural completeness and transposition capacity. It has been proposed that selection is the major force for maintaining sequence (e.g., LTR) conservation between nonautonomous elements and their autonomous counterpar...

Signals derived from the microenvironment contribute greatly to tumorigenesis . The underlying mechanism requires thorough investigation. Here, we use Drosophila testis as a model system to address this question, taking the advantage of the ease to distinguish germline and somatic cells and to track the cell numbers. In an EMS mutagenesis screen, we identified Rab5, a key factor in endocytosis,...

We consider an integral variational control system on a Banach space X and we study the connections between its uniform exponential stability and the I R , X , O R , X stability, where I andO are Banach function spaces. We identify the viable classes of input spaces and output spaces related to the exponential stability of systems and provide optimization techniques with respect to the input sp...

In this paper several necessary and sufficient conditions for existence of stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation (RDE) are presented. The conditions are reduced to existence of a solution to the corresponding Riccati type matrix inequality, or to existence of exponential dichotomy for the associated Hamiltonian linear differential sy...

This manuscript develops a novel understanding of nonpolar solutions the discrete Painlevé I equation (dP1). As nonautonomous counterpart an analytically completely integrable difference equation, this system is endowed with rich dynamical structure. In addition, its solutions, which grow without bounds as iteration index $n$ increases, are particular relevance to other areas mathematics. We co...

A system of nonautonomous partial differential equations describing the steady flow of an incompressible fluid is considered. The existence of a strong solution of that system is proved under suitable assumptions on the data. In the 2D-case this solution turns out to be of class C1,α. §

Stabilization to a trajectory for the monodomain equations, a coupled nonlinear PDE-ODE system, is investigated. The results rely on stabilization of linear first-order in time nonautonomous evolution equations combined with stabilizability results for the linearized monodomain equations and a fixed point argument to treat local stabilizability of the nonlinear system. Numerical experiments for...

Traditional assumptions in the simple chemostat model include fixed availability of the nutrient and its supply rate, and fast flow rate to avoid wall growth. However, these assumptions become unrealistic when the availability of a nutrient depends on the nutrient consumption rate and input nutrient concentration and when the flow rate is not fast enough. In this paper, we relax these assumptio...