A new method is presented for the analysis of limit cycle oscillations in mixed-feedback systems. The calculation reformulated as zero finding a mixed-monotone relation, that is, difference two maximally monotone relations. problem can then be solved efficiently by borrowing existing algorithms minimize convex functions. potential illustrated on classical Van der Pol oscillator.

Being motivated in terms of mathematical concepts from the theory of electrical networks, Klein & Ivanciuc introduced and studied a new graph-theoretic cyclicity index–the global cyclicity index (Graph cyclicity, excess conductance, and resistance deficit, J. Math. Chem. 30 (2001) 271–287). In this paper, by utilizing techniques from graph theory, electrical network theory and real analysis, we...

Let P be a monotone property of directed graphs on n vertices, and let P n denote the abstract simplicial complex whose simplices are the edge sets of graphs having property P. We prove that: 1. If \P = acyclic" then P n is homotopy equivalent to the (n ? 2)-sphere. 2. If \P = not strongly connected" then P n has the homotopy type of a wedge of (n ? 1)! spheres of dimension 2n ? 4. The lattice ...

Moody, P. J. and A. W. Roscoe, Acyclic monotone normality, Topology and its Applications 47 (1992) 53-67. A space X is acyclic monotonically normal if it has a monotonically normal operator M(., .) such that for distinct points x,,, ,x._, in X and x, =x,], n::i M(x,, X\{x,+,}) = (d. It is a property which arises from the study of monotone normality and the condition “chain (F)“. In this paper i...

In the investigation of boundary value problems the construction of a twosided inclusion of the solution can be as important as a numerical approximation of the solution itself. In the present paper we analyze a monotone discretization technique of higher order based upon piecewise interpolation and shifting such that bounding upper and lower solutions are obtained. The monotone discretization ...

Abstract We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that general approach from [P. Heid and T. P. Wihler, Adaptive linearization Galerkin methods problems, Math. Comp. 89 2020, 326, 2707–2734; On convergence adaptive linearized methods, Calcolo 57 Paper No. 24] satisfies an energy contraction property context (abs...

Ding, G., Monotone clutters, Discrete Mathematics 119 (1993) 67-77. A clutter is k-monotone, completely monotone or threshold if the corresponding Boolean function is k-monotone, completely monotone or threshold, respectively. A characterization of k-monotone clutters in terms ofexcluded minors is presented here. This result is used to derive a characterization of 2-monotone matroids and of 3-m...