Time response of a scalar dynamical system with multiple delays via   Lambert W functions
  In this work, we establish the response of scalar systems with multiple discrete delays based on the Laplace transform. The time response function is expressed as the sum of infinite series of exponentials acting on eigenvalues inside countable branches of the Lambert W functions. Eigenvalues in each branch of Lambert W function are computed by a numerical iteration. Numerical examples are presented to illustrate the results obtained. 
Shuo-Tsung Chen, Shun-Pin Hsu, Huang-Nan Huang, and Bin-Yan Yang
math.DS