arXiv:2603.17026v1 Announce Type: new
Abstract: In this paper we expand the concept of biological speciation by symmetry breaking of Golubitsky and Stewart to the case of three clades in which N populations following the same dynamical laws can separate. The underlying differential equation is based on a fifth order polynomial of a trait variable with first or second order coupling. We present some general strategies to find all possible steady states and their stabilities. Numerical data are given for a specific system. We show the locations of three-clade distributions in dependence on the coupling and an environmental parameter. The results show a decrease of the number of stable states with higher coupling and a higher probability of ending in a three-clade state for larger N. Limits and potentials of the approach if zero roots for the trait variable occur are discussed.
Volumetric Ergodic Control
arXiv:2511.11533v2 Announce Type: replace-cross Abstract: Ergodic control synthesizes optimal coverage behaviors over spatial distributions for nonlinear systems. However, existing formulations model the robot as a