  The paper presents a review of the studies that were conducted at Energy
Systems Institute (ESI) SB RAS in the field of mathematical modeling of
nonlinear input-output dynamic systems with Volterra polynomials. The first
part presents an original approach to identification of the Volterra kernels.
The approach is based on setting special multiparameter families of piecewise
constant test input signals. It also includes a description of the respective
software; presents illustrative calculations on the example of a reference
dynamic system as well as results of computer modeling of real heat exchange
processes. The second part of the review is devoted to the Volterra polynomial
equations of the first kind. Studies of such equations were pioneered and have
been carried out in the past decade by the laboratory of ill-posed problems at
ESI SB RAS. A special focus in the paper is made on the importance of the
Lambert function for the theory of these equations.
