Simplex type differential inclusions (Q1588788)

The author reveals modelling simplifications and ease of numerical calculation for the differential inclusion \(\dot x\in V(x)\) in case \(V(x)\) is the \(p\)-dimensional simplex with vertices \(v_0(x)\), \dots, \(v_p(x)\). The investigation relies on the \(\tau\)-family of differential inclusions \(\dot x=X_\tau(x)\) with \(X_\tau=\tau^0v_0+\cdots+\tau^kv_k\) and \(\tau\) ranges over the standard \(p\)-dimensional simplex.