We establish a connection between solutions to a broad class of large systems of ordinary differential equations and solutions to retarded differential equations. We prove that solving the Cauchy problem for systems of ordinary differential equations reduces to solving the initial value problem for a retarded differential equation as the number of equations increases unboundedly. In particular, the class of systems under consideration contains a system of differential equations which arises in modeling of multiphase synthesis.In this article we continue to study connection between large systems of ordinary differential equations and retarded differential equations(1.1)The first result in this direction was obtained while studying a system of differential equations which arises in modeling of multiphase synthesis without bifurcation [1,2]. This system has the form(1.2)In [1] it was established that if we let the number n of equations in system (1.2) increase unboundedly and consider only the last components of the solution to the Cauchy problem with the zero initial data x| t=0 = 0 then we obtain a uniformly converging sequencex n n (t) → y(t), t ∈ [0, T ], as n → ∞; moreover, the limit function y(t) satisfies the identityConsequently, the function y(t) is a solution to the retarded differential equation (1.1), where the righthand side has the form f (t, u, v) = −θu + g(v).
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