Solution of Simultaneous Higher Order Equations Based on DNA Strand Displacement Circuit

Implementation of an Ultrasensitive Biomolecular Controller for Enzymatic Reaction Processes With Delay Using DNA Strand Displacement

In this article, a set of abstract chemical reactions has been employed to construct a novel nonlinear biomolecular controller, i.e, the Brink controller (BC) with direct positive autoregulation (DPAR) (namely BC-DPAR controller). In comparison to dual rail representation-based controllers such as the quasi sliding mode (QSM) controller, the BC-DPAR controller directly reduces the number of CRNs required for realizing an ultrasensitive input-output response because it does not involve the subtraction module, reducing the complexity of DNA implementations. Then, the action mechanism and steady-state condition constraints of two nonlinear controllers, BC-DPAR controller and QSM controller, are investigated further. Considering the mapping relationship between CRNs and DNA implementation, a CRNs-based enzymatic reaction process with delay is constructed, and a DNA strand displacement (DSD) scheme representing time delay is proposed. The BC-DPAR controller, when compared to the QSM controller, can reduce the number of abstract chemical reactions and DSD reactions required by 33.3% and 31.8%, respectively. Finally, an enzymatic reaction scheme with BC-DPAR controller is designed using DSD reactions. According to the findings, the enzymatic reaction process's output substance can approach the target level at a quasi-steady state in both delay-free and non-zero delay conditions, but the target level can only be achieved during a finite-time period, mainly due to the fuel stand depletion.

A Novel 3-D Jerk System, Its Bifurcation Analysis, Electronic Circuit Design and a Cryptographic Application

This paper introduces a new chaotic jerk system with three cubic nonlinear terms. The stability properties of the three equilibrium points of the proposed jerk system are analyzed in detail. We show that the three equilibrium points of the new chaotic jerk system are unstable and deduce that the jerk system exhibits self-excited chaotic attractors. The bifurcation structures of the proposed jerk system are investigated numerically, showing period-doubling, periodic windows and coexisting bifurcations. An electronic circuit design of the proposed jerk system is designed using PSPICE. As an engineering application, a new image-encryption approach based on the new chaotic jerk system is presented in this research work. Experimental results demonstrate that the suggested encryption mechanism is effective with high plain-image sensitivity and the reliability of the proposed chaotic jerk system for various cryptographic purposes.