The motivation for this work is to formulate a control design method for a pneumatic system with discrete input values (resulting from the use of binary or three-position solenoid valves) that addresses the time-delay that is often associated with the flow state of solenoid on/off valves. This method is shown to be applicable to a general class of nonlinear, nonautonomous systems subject to pos...

The existence and uniqueness of a variational solution are proved for the following nonautonomous nonclassical diffusion equation ut − εΔut − Δu f u g x, t , ε ∈ 0, 1 , in a noncylindrical domain with homogeneous Dirichlet boundary conditions, under the assumption that the spatial domains are bounded and increase with time. Moreover, the nonautonomous dynamical system generated by this class of...

In this paper, we systematically study the dynamics of a nonautonomous predator–prey system with the Beddington–DeAngelis functional response. The explorations involve the permanence, extinction, global asymptotic stability (general nonautonomous case); the existence, uniqueness and stability of a positive (almost) periodic solution and a boundary (almost) periodic solution for the periodic (al...

We wish to generalize van Kampen’s theorem to include nonautonomous master equations. Such a theorem is important in applications, e.g. in ion channel kinetics, where subunit opening and closing rates are subject to external forces (e.g. membrane voltage) and are therefore often unavoidably nonautonomous. There are two issues to consider when moving to the nonautonomous case. The first is that,...