We consider nonlinear impulsive systems on Banach spaces subjected to disturbances and look for dwell-time conditions guaranteeing the ISS property. In contrary many existing results our cover case where both continuous discrete dynamics can be unstable simultaneously. Lyapunov type methods are used this purpose. The effectiveness of approach is illustrated a rather nontrivial example, which fe...

Abstract We analyze travelling wave (TW) solutions for nonlinear systems consisting of an ODE coupled to a degenerate PDE with diffusion coefficient that vanishes as the solution tends zero and blows up it approaches its maximum value. Stable TW such have previously been observed numerically well in biological experiments on growth cellulolytic biofilms. In this work, we provide analytical just...

Purpose A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement resulting system differential algebraic equations reformulated into ordinary (ODE). The ODE integrated in time by explicit integration schemes. purpose this pape...

In this article, we study the landscape of an online nonconvex optimization problem, for which input data vary over time and solution is a trajectory rather than single point. To understand complexity finding global introduce notion spurious (i.e., nonglobal) local trajectory as generalization ...

It is known that non-isomorphic coupled cell networks can have equivalent dynamics. Such networks are said to be ODE-equivalent and are related by a linear algebra condition involving their graph adjacency matrices. A network in an ODE-equivalence class is said to be minimal if it has a minimum number of edges. When studying a given network in an ODE-class it can be of great value to study inst...