The bifurcations in a four-variable ODE model of an SIS type epidemic on an adaptive network are studied. The model describes the propagation of the epidemic on a network where links (or edges) of different type (i.e. SI,II and SS ) can be activated or deleted according to a simple rule consisting of random link activation and deletion. In the case when II links cannot be neither deleted nor cr...

We consider the shallow water equations with non-flat bottom topography. The smooth solutions of these equations are energy conservative, whereas weak solutions are energy stable. The equations possess interesting steady states of lake at rest as well as moving equilibrium states. We design energy conservative finite volume schemes which preserve (i) the lake at rest steady state in both one an...

Abstract Nature is never at a steady state. Natural history generated by ever-new and ever-interacting forces that produce continuous changes. At virtually all timescales, the geological record shows these changes do not cancel each other out and, thus, state utopic. However, we need of equilibrium as starting point for modelling Nature, steady-state condition widely used reference in idealisat...

In this paper, we prove that a mean system utilization smaller than one is necessary condition for the feasibility of real-time systems. Such systems are defined as stable . Stable have two distinct states: transient state, followed by steady-state where same distribution response times repeate...

We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations linearized about a possibly unstable steady state. The reduced-order models are obtained using an approximate balanced truncation method that retains the most controllable and observable modes of the system. The original method is valid only for stable linear systems, a...