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By introducing some parameters perturbed by white noises, we propose a class of stochastic inertial neural networks in random environments. Constructing two Lyapunov–Krasovskii functionals, we establish the mean-square exponential input-to-state stability on the addressed model, which generalizes and refines the recent results. In addition, an example with numerical simulation is carried out to support the theoretical findings. [ABSTRACT FROM AUTHOR]

Considering stochastic perturbations of white and color noises, we introduce the Markov switched stochastic Nicholson-type delay system with patch structure. By constructing a traditional Lyapunov function we show that solutions of the addressed system are not only positive, but also do not explode to infinity in finite time and, in fact, are ultimately bounded. Then we estimate its ultimate boundedness, moment, and Lyapunov exponent. Finally, we present an example of numerical simulations to verify theoretical results. [ABSTRACT FROM AUTHOR]

By using the Krasnoselskii fixed point theorem in a cone, we investigate the existence of two positive periodic solutions of the generalized delay differential neoclassical growth model with periodic coefficients and delays. Moreover, we give an example to demonstrate the theoretical result. [ABSTRACT FROM AUTHOR]

The paper is concerned with periodic solutions of a model of gene regulatory system with time-varying coefficients and delays. We establish some sufficient conditions for the existence, positivity, and permanence of solutions, which help to derive the global exponential stability of positive periodic solutions for this model. Our method depends on differential inequality technique and Lyapunov functional. At last, we give an example and its numerical simulations to verify theoretical results. [ABSTRACT FROM AUTHOR]

Focusing on delay differential neoclassical growth model in random environments, we introduce the stochastic model to describe the dynamics of the long-run behavior of the economy with a parameter perturbed by white noises. We prove that the global positive solution exists uniquely and estimate its ultimate boundedness in mean and sample Lyapunov exponent. Finally, some numerical tests are given to illustrate theoretical results. [ABSTRACT FROM AUTHOR]