Spontaneous switching events in most characterized genetic switches are rare, resulting in extremely stable epigenetic properties. We show how simple arguments lead to theories of the rate of such events much like the absolute rate theory of chemical reactions corrected by a transmission factor. Both the probability of the rare cellular states that allow epigenetic escape and the transmission f...

This paper presents some new results for the absolute stability of Hopfield neural networks with activation functions chosen from sigmoidal functions which have unbounded derivatives. Detailed discussions are also given to the relation and difference of absolute stabilities between neural networks and Lurie systems with multiple nonlinear controls. Although the basic idea of the absolute stabil...

The concept of parametric stability is extended to include Lur’e-type nonlinear control systems with uncertain parameters and constant reference inputs. Conditions for parametric absolute stability are derived, which guarantee that the system remains stable despite uncertainty of equilibrium location caused by parametric uncertainties and values of the reference input. The conditions can be tes...

In this paper, the robust absolute stability property of multi-agent systems by transforming the original system into a Lur’e system is presented. Different configurations of multi-agent systems are considered, which they include parametric uncertainty. These systems are primarily stabilized by applying robust design techniques to further verify the absolute stability property of the closed loo...

This paper studies the problem of robust absolute stability of a class of nonlinear discrete-time systems with time-varying matrix uncertainties of polyhedral type and multiple time-varying sector nonlinearities. By using the variational method and the Lyapunov second method, criteria for robust absolute stability are obtained in different forms for the class of systems under consideration. Spe...