Abstract
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.
Highlights
In order to explain the complex dynamic behavior of genetic regulatory systems, the authors of [ ] presented a model of ordinary differential system for the transcript factors (TFs)
In the real-world phenomena, the periodic variation of the environment plays a pivotal role in determining the dynamics, so that some classic models, such as the Nicholson blowflies model [, ], hematopoiesis model [, ], etc., have been generalized to the nonautonomous nonlinear delay differential equation with time-varying coefficients and delays. It is worth studying the model of gene regulatory system with time-varying coefficients and delays
To the best of our knowledge, rare authors studied the problems of the global exponential stability of positive periodic solutions for genetic regulatory system with timevarying coefficients and delays
Summary
In order to explain the complex dynamic behavior of genetic regulatory systems, the authors of [ ] presented a model of ordinary differential system for the transcript factors (TFs). In the real-world phenomena, the periodic variation of the environment (e.g., temperature, moisture, pressure, seasonal effects of weather, reproduction, food supplies, mating habits, etc.) plays a pivotal role in determining the dynamics, so that some classic models, such as the Nicholson blowflies model [ , ], hematopoiesis model [ , ], etc., have been generalized to the nonautonomous nonlinear delay differential equation with time-varying coefficients and delays. It is worth studying the model of gene regulatory system with time-varying coefficients and delays. K + l – there exists a unique positive global solution x(t; t , φ) to initial value problem
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