On Proving the Absence of Oscillations in Models of Genetic Circuits

Chemical Reaction Systems, Computer Algebra and Systems Biology

“…See [29] for a closely related work. Our algorithm was successfully applied over a more complicated model [6,5], featuring two genes, arising from the modeling problem of the circadian clock of the green algae Ostreococcus tauri [12].…”

Investigating Generic Methods to Solve Hopf Bifurcation Problems in Algebraic Biology

“…Symbolic methods to investigate Hopf bifurcation problems of vector fields arising in the context of algebraic biology have recently obtained renewed attention [1][2][3]. A major reason for this attention is the relationship between Hopf bifurcation fixed points and the occurrence of oscillations.…”

“…A major reason for this attention is the relationship between Hopf bifurcation fixed points and the occurrence of oscillations. Although this relationship is subtle-we refer to [1,3] for nice introductions containing further referencesthe topic of investigating "oscillations" in systems for biologically or chemically relevant values of parameters is of such great interest that considerable work has been done to investigate various biological and chemical systems with respect to Hopf bifurcation fixed points, see e.g. [4][5][6][7][8] to mention only some.…”

“…the ones investigated in [1,2], have not been fully algorithmic up to now but required a sequence of symbolic computation intervened with ad hoc insights and decisions made by a human, and sometimes of sophisticated coordinate transforms. The aim of this paper is to demonstrate how to proceed fully algorithmically for the examples discussed there.…”

“…We can reconstruct the results of [1] in some seconds of computation time. Also the main example given in [2] could be handled in principle-without using the sophisticated coordinate transform used there.…”