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This paper considers a single-population model with age structure andpsychological effects in a polluted environment. We divide the singlepopulation into two stages of larval and adult structure. The model usesLogistic input, and the larvae are converted into adult bodies by constantratio. We only consider adulthood. The role of psychological effects makes thecontact between adult and environmental toxins a functional form, while thecontact between larvae and environmental toxins is linear.  For the deterministic model embodied as a nonlinear time-varying system, wediscuss the asymptotic stability of the system by Lyapunov one-timeapproximation theory, and give a sufficient condition for stability to beestablished.  Considering that the contact rate between biological and environmental toxinsin nature is not always constant, we make the contact rate interfere with whitenoise, and then modify the contact rate into a stochastic process, thusestablishing a corresponding random single-population model. According to It\^oformula and Lyapunov in the function method, we first prove the existence ofglobally unique positive solutions for stochastic models under arbitraryinitial conditions, and then give sufficient conditions for weak averagelong-term survival and random long-term survival for single populations in theexpected sense.

Single-species population models with age structure and psychological effect in a polluted environment