We have investigated Turing pattern formation through linear stability analysis and numerical simulations in a two-species reaction–diffusion system in which a fractional order temporal derivative operates on both species, and on both the diffusion term and the reaction term. The order of the fractional derivative affects the time onset of patterning in this model system but it does not affect ...

Motivated by biochemical reaction networks, a generalization of the classical secant condition for stability analysis cyclic interconnected commensurate fractional-order systems is provided. The main result presents sufficient networks interconnection when digraph describing network conforms to single circuit. becomes necessary under special situation where coupling weights are uniform. We then...

Living systems rely on complex networks of chemical reactions to control the concentrations of molecules in space and time. Despite the enormous complexity in biological networks, it is possible to identify network motifs that lead to functional outputs such as bistability or oscillations. One of the greatest challenges in chemistry is the creation of such functionality from chemical reactions....

In many stochastic simulations of biochemical reaction networks, it is desirable to "coarse grain" the reaction set, removing fast reactions while retaining the correct system dynamics. Various coarse-graining methods have been proposed, but it remains unclear which methods are reliable and which reactions can safely be eliminated. We address these issues for a model gene regulatory network tha...

The determination of reaction pathways is one of the most important functions that should be performed in exploring the kinetics of catalyzed chemical reactions or biochemical reactions, the latter being generally catalyzed by enzymes. It is proven that the terms, "type-I extreme pathway" and "structurally minimal pathway", both introduced to characterize the kinetics of a catalyzed reaction ar...

This paper reports the first example of the use of an enzymatic reaction to generate a photoresponsive hydrogelator, which represents a convenient route to expand the scope of optically controlled molecular self-assembly in water.

) Time-Scaled Stochastic Input to Biochemical Reaction Networks by Rachel L. Thomas Department of Mathematics Duke University

In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on whi...

Nowadays, due to the high expectations of customers in meeting their demand and the competition environment among service providers, employers are working to provide customers with new methods in the shortest possible time and in the best possible way to attract customer’s satisfaction and maximize profits. In this paper, the orienteering problem with variable profits, fractional objective func...