The quest to mathematically realize the complex dynamics of neuromorphic processes has led to the development of differential models that approximate neural signal behavior within controlled dynamical systems. Based on the maximum entropy principle and the tensor product of Hilbert spaces, we examine the solvability of the problem concerning the existence of a differential realization of nonlinear neuromorphic dynamic processes in a class of bilinear nonstationary ordinary differential equations of the second order (with and without delay) in a separable Hilbert space. Additionally, we analyze the metric conditions of continuity of the projectivization of the entropy Rayleigh–Ritz operator, and compute the fundamental group of its compact image. These problems belong to the class of nonstationary operator inverse problems for evolutionary equations in an infinite-dimensional Hilbert space. They provide new insights into the development of the theory of nonlinear inverse problems for higher-order multilinear non-autonomous differential equations with a “delay factor,” which cannot be solved with respect to the higher-order derivatives. The results obtained in this study may be applicable to the precision modeling of differential equations of nonlinear neurodynamics, providing a meta-basis for the analysis of the cognitive activity of local neuropopulations under investigation.