Ket Hing Chong;Sandhya Samarasinghe;Don Kulasiri;Jie Zheng(2015).“Computational techniques in mathematical modelling of biological switches”.MODSIM2015: 578–584. For detailed techniques of mathematical modelling of bistability, see the tutorial by Chong et al. (2015) https://www.mssanz.org.au/modsim2015/C2/chong.pdf The tutorial provides a simple example illustration of bistability using a synthetic toggle switch proposed in Collins,James J.;Gardner,Timothy S.;Cantor,Charles R.(2000).“Construction of a genetic toggle switch in Escherichia coli”.Nature403(6767): 339–42.Bibcode:2000Natur.403..339G.doi:10.1038/35002131.PMID10659857.. The tutorial also uses the dynamical system software XPPAUT http://www.math.pitt.edu/~bard/xpp/xpp.html to show practically how to see bistability captured by a saddle-node bifurcation diagram and the hysteresis behaviours when the bifurcation parameter is increased or decreased slowly over the tipping points and a protein gets turned 'On' or turned 'Off'.
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Ket Hing Chong;Sandhya Samarasinghe;Don Kulasiri;Jie Zheng(2015).“Computational techniques in mathematical modelling of biological switches”.MODSIM2015: 578–584. For detailed techniques of mathematical modelling of bistability, see the tutorial by Chong et al. (2015) https://www.mssanz.org.au/modsim2015/C2/chong.pdf The tutorial provides a simple example illustration of bistability using a synthetic toggle switch proposed in Collins,James J.;Gardner,Timothy S.;Cantor,Charles R.(2000).“Construction of a genetic toggle switch in Escherichia coli”.Nature403(6767): 339–42.Bibcode:2000Natur.403..339G.doi:10.1038/35002131.PMID10659857.. The tutorial also uses the dynamical system software XPPAUT http://www.math.pitt.edu/~bard/xpp/xpp.html to show practically how to see bistability captured by a saddle-node bifurcation diagram and the hysteresis behaviours when the bifurcation parameter is increased or decreased slowly over the tipping points and a protein gets turned 'On' or turned 'Off'.
Mathias L. Heltberg, Sandeep Krishna, and Mogens H. Jensen(2017).“Time Correlations in Mode Hopping of Coupled Oscillators”.Journal of Statistical Physics167: 792-805.doi:10.1007/s10955-017-1750-x.
Elf,J.;Ehrenberg,M.(2004).“Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases”.Systems Biology1(2): 230–236.doi:10.1049/sb:20045021.PMID17051695.
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A.G. Dunning, N. Tolou, P.J. Pluimers, L.F. Kluit, and J.L. Herder(2012).“Bi-stable Compliant Mechanisms: Correction for Finite Element Modeling, Tuning the Stiffness and Preloading Incorporation”.Journal of Mechanical Design134(8): 084502.doi:10.1115/1.4006961.
Ket Hing Chong;Sandhya Samarasinghe;Don Kulasiri;Jie Zheng(2015).“Computational techniques in mathematical modelling of biological switches”.MODSIM2015: 578–584. For detailed techniques of mathematical modelling of bistability, see the tutorial by Chong et al. (2015) https://www.mssanz.org.au/modsim2015/C2/chong.pdf The tutorial provides a simple example illustration of bistability using a synthetic toggle switch proposed in Collins,James J.;Gardner,Timothy S.;Cantor,Charles R.(2000).“Construction of a genetic toggle switch in Escherichia coli”.Nature403(6767): 339–42.Bibcode:2000Natur.403..339G.doi:10.1038/35002131.PMID10659857.. The tutorial also uses the dynamical system software XPPAUT http://www.math.pitt.edu/~bard/xpp/xpp.html to show practically how to see bistability captured by a saddle-node bifurcation diagram and the hysteresis behaviours when the bifurcation parameter is increased or decreased slowly over the tipping points and a protein gets turned 'On' or turned 'Off'.
Ket Hing Chong;Sandhya Samarasinghe;Don Kulasiri;Jie Zheng(2015).“Computational techniques in mathematical modelling of biological switches”.MODSIM2015: 578–584. For detailed techniques of mathematical modelling of bistability, see the tutorial by Chong et al. (2015) https://www.mssanz.org.au/modsim2015/C2/chong.pdf The tutorial provides a simple example illustration of bistability using a synthetic toggle switch proposed in Collins,James J.;Gardner,Timothy S.;Cantor,Charles R.(2000).“Construction of a genetic toggle switch in Escherichia coli”.Nature403(6767): 339–42.Bibcode:2000Natur.403..339G.doi:10.1038/35002131.PMID10659857.. The tutorial also uses the dynamical system software XPPAUT http://www.math.pitt.edu/~bard/xpp/xpp.html to show practically how to see bistability captured by a saddle-node bifurcation diagram and the hysteresis behaviours when the bifurcation parameter is increased or decreased slowly over the tipping points and a protein gets turned 'On' or turned 'Off'.
Elf,J.;Ehrenberg,M.(2004).“Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases”.Systems Biology1(2): 230–236.doi:10.1049/sb:20045021.PMID17051695.
Ket Hing Chong;Sandhya Samarasinghe;Don Kulasiri;Jie Zheng(2015).“Computational techniques in mathematical modelling of biological switches”.MODSIM2015: 578–584. For detailed techniques of mathematical modelling of bistability, see the tutorial by Chong et al. (2015) https://www.mssanz.org.au/modsim2015/C2/chong.pdf The tutorial provides a simple example illustration of bistability using a synthetic toggle switch proposed in Collins,James J.;Gardner,Timothy S.;Cantor,Charles R.(2000).“Construction of a genetic toggle switch in Escherichia coli”.Nature403(6767): 339–42.Bibcode:2000Natur.403..339G.doi:10.1038/35002131.PMID10659857.. The tutorial also uses the dynamical system software XPPAUT http://www.math.pitt.edu/~bard/xpp/xpp.html to show practically how to see bistability captured by a saddle-node bifurcation diagram and the hysteresis behaviours when the bifurcation parameter is increased or decreased slowly over the tipping points and a protein gets turned 'On' or turned 'Off'.