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A differential equation of a special form, which contains two control functions  f  and g and one delayed argument, is analyzed. This equation has a wide application in biology for the description of dynamic processes in population, physiological, metabolic, molecular-genetic, and other applications. Specific numerical examples show the correlation between the properties of the one-dimensional mapping, which is generated by the ratio   f /g , and the presence of chaotic dynamics for such equation. An empirical criterion is formulated that allows one to predict the presence of a chaotic potential for a given equation by the properties of the one-dimensional mapping   f /g .

On The Correlation between Properties of One-Dimensional Mappings of Control Functions and Chaos in a Special Type Delay Differential Equation