Hopf bifurcation analysis for genetic regulatory networks with two delays

Global stability analysis of fractional-order gene regulatory networks with time delay

Fractional-order gene regulatory networks with time delay (DFGRNs) have proven that they are more suitable to model gene regulation mechanism than integer-order. In this paper, a novel DFGRN is proposed. The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions. On this basis, the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN, and the stability conditions are dependent on the fractional-order [Formula: see text]. Finally, numerical simulations show that the obtained results are reasonable.

State Estimation for Delayed Genetic Regulatory Networks With Reaction-Diffusion Terms

This paper addresses the problem of state estimation for delayed genetic regulatory networks (DGRNs) with reaction-diffusion terms using Dirichlet boundary conditions. The nonlinear regulation function of DGRNs is assumed to exhibit the Hill form. The aim of this paper is to design a state observer to estimate the concentrations of mRNAs and proteins via available measurement techniques. By introducing novel integral terms into the Lyapunov-Krasovskii functional and by employing the Wirtinger-type integral inequality, the convex approach, Green's identity, the reciprocally convex approach, and Wirtinger's inequality, an asymptotic stability criterion of the error system was established in terms of linear matrix inequalities (LMIs). The stability criterion depends upon the bounds of delays and their derivatives. It should be noted that if the set of LMIs is feasible, then the desired observation of DGRNs is possible, and the state estimation can be determined. Finally, two numerical examples are presented to illustrate the availability and applicability of the proposed scheme design.

Bogdanov-Takens bifurcation in a neutral BAM neural networks model with delays

In this study, the authors first discuss the existence of Bogdanov-Takens and triple zero singularity of a five neurons neutral bidirectional associative memory neural networks model with two delays. Then, by utilising the centre manifold reduction and choosing suitable bifurcation parameters, the second-order and the third-order normal forms of the Bogdanov-Takens bifurcation for the system are obtained. Finally, the obtained normal form and numerical simulations show some interesting phenomena such as the existence of a stable fixed point, a pair of stable non-trivial equilibria, a stable limit cycles, heteroclinic orbits, homoclinic orbits, coexistence of two stable non-trivial equilibria and a stable limit cycles in the neighbourhood of the Bogdanov-Takens bifurcation critical point.

Finite-Time Stability Analysis of Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays

This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.