Wu X,You X,Wang B.Structure-Preserving Algorithms for Oscillatory Differential Equations[M].Heidelberg:Springer,2013:1-26
[4]
Fang Y,You X,Ming Q.Exponentially fitted two-derivative Runge-Kutta methods for Schr?dinger equation[J].International Journal of Modern Physics C,2013,24,Article ID 1350073,9 pages
Zhang Y,Che H,Fang Y,et al.A new trigonometrically fitted two-derivative Runge-Kutta method for the numerical solution of the Schr?dinger equation and related problems[J].Journal of Applied Mathematics,2013,2013,Article ID 937858,9 pages
Widder S,Schicho J,Schuster P.Dynamic patterns of gene regulationⅠ:simple two-gene systems[J].Journal of Theoretical Biology,2007,246:395-419
[9]
Goldbeter A.Biochemical Oscillations and Cellular Rhythms:The Molecular Bases of Periodic and Chaotic Behavior[M].Cambridge:Cambridge University Press,1996:459-490
[10]
Glossop N R J,Lyons L C,Hardin P E.Interlocked feed back loops within the Drosophila circadian oscillator[J].Science,1999,286:766-768
[11]
Leloup J C,Goldbeter A.Chaos and birhythmicity in a model for circadian oscillations of the PER and TIM proteins in Drosophila[J].Journal of Theoretical Biology,1999,198:445-459
[12]
Gérard C,Gonze D,Goldbeter A.Dependence of the period on the rate of protein degradation in minimal models for circadian oscillations[J].Philosophical Transaction of Royal Society A,2009,367:4665-4683
[13]
Zhang Y,Ling J,Yuan C,et al.A role for Drosophila ATX2 in activation of PER translation and circadian behavior[J].Science,2013,340:879-882
[14]
Lim C,Allada R.ATAXIN-2 activates PERIOD translation to sustain circadian rhythms in Drosophila[J].Science,2013,340:875-879
[15]
Goodwin B C.Oscillatory behaviour in enzymatic control processes[J].Advances in Enzyme Regulation,1965,3:425-438
[16]
Hardin P E,Hall J C,Rosbash M.Circadian oscillations in period gene mRNA levels are transcriptionally regulated[J].Proc Natl Acad Sci USA,1992,89:11711-11715
[17]
Goldbeter A.A model for circadian oscillations in the Drosophila period protein(PER)[J].Proceedings of Royal Society London B,1995,261:319-324
[18]
Leloup J C,Goldbeter A.Modeling the molecular regulatory mechanism of circadian rhythms in Drosophila[J].BioEssays,2000,22:84-93
[19]
You X.Limit-cycle-preserving simulation of gene regulatory oscillators[J].Discrete Dynamics in Nature and Society,2012,2012,Article ID 673296,22 pages
[20]
Chan R P K,Tsai A Y J.On explicit two-derivative Runge-Kutta methods[J].Numerical Algorithms,2010,53:171-194
[21]
Butcher J C.Numerical Methods for Ordinary Differential Equations[M].2nd ed.Chichester:John Wiley and Sons Ltd.,2008:137-316