Study of genetic regulatory networks with Stepanov-like pseudo-weighted almost automorphic coefficients

Random periodic sequence of globally mean-square exponentially stable discrete-time stochastic genetic regulatory networks with discrete spatial diffusions

<abstract><p>This paper regards the dual effects of discrete-space and discrete-time in stochastic genetic regulatory networks via exponential Euler difference and central finite difference. Firstly, the global exponential stability of such discrete networks is investigated by using discrete constant variation formulation. In particular, the optimal exponential convergence rate is explored by solving a nonlinear optimization problem under nonlinear constraints, and an implementable computer algorithm for computing the optimal exponential convergence rate is given. Secondly, random periodic sequence for such discrete networks is investigated based on the theory of semi-flow and metric dynamical systems. The researching findings show that the spatial diffusions with nonnegative intensive coefficients have no influence on global mean square boundedness and stability, random periodicity of the networks. This paper is pioneering in considering discrete spatial diffusions, which provides a research basis for future research on genetic regulatory networks.</p></abstract>

Stability analysis and synchronized control of fuzzy Mittag-Leffler discrete-time genetic regulatory networks with time delays

Exponential Euler differences for semi-linear differential equations of first order have got rapid development in the past few years and a variety of exponential Euler difference methods have become very significant researching topics. In allusion to fuzzy genetic regulatory networks of fractional order, this paper firstly establishes a novel difference method called Mittag-Leffler Euler difference, which includes the exponential Euler difference. In the second place, the existence of a unique global bounded solution and equilibrium point, global exponential stability and synchronization of the derived difference models are investigated. Compared with the classical fractional Euler differences, fuzzy Mittag-Leffler discrete-time genetic regulatory networks can better depict and retain the dynamic characteristics of the corresponding continuous-time models. What’s more important is that it starts a new avenue for studying discrete-time fractional-order systems and a set of theories and methods is constructed in studying Mittag-Leffler discrete models.