Erratum to: Stable periodicity and negative circuits in differential systems (Journal of Mathematical Biology, (2011), 63, 593-600, 10.1007/s00285-010-0388-y);Stable periodicity and negative circuits in differential systems

Journal of Mathematical Biology

Volumn 63, Issue 3, 2011, Pages 593-600

  Richard, Adrien ^a   Comet, Jean Paul ^a  

^a UNIVERSITY OF NICE SOPHIA ANTIPOLIS   (France)

Author keywords

Feedback circuit; Interaction graph; Jacobian matrix; Oscillation; Regulatory network

Indexed keywords

EID: 80051665924     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-014-0855-y     Document Type: Erratum

References (13)

1. Braun M (1993) Differential equations and their applications. Springer, Berlin.
2. Cinquin P, Demongeot J (2002) Positive and negative feedback: striking a balance between necessary antagonists. J Theor Biol 216: 229-241.
3. de Jong H (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comp Biol 9: 67-103.
4. Gouzé JL (1998) Positive and negative circuits in dynamical systems. J Biol Syst 6: 11-15.
5. Kaufman M, Soulé C, Thomas R (2007) A new necessary condition on interaction graphs for multistationarity. J Theor Biol 248: 675-685.
6. Perko L (2002) Differential equations and dynamical systems. Springer, Berlin.
7. Plahte E, Mestl T, Omholt WS (1995) Feedback circuits, stability and multistationarity in dynamical systems. J Biol Syst 3: 409-413.
8. Remy E, Ruet P, Thieffry D (2008) Graphics requirement for multistability and attractive cycles in a boolean dynamical framework. Adv Appl Math 41: 335-350.
9. Richard A (2010) Negative circuits and sustained oscillations in asynchronous automata networks. Adv Appl Math 44: 378-392.
10. Richard A, Comet JP (2007) Necessary conditions for multistationarity in discrete dynamical systems. Discrete Appl Math 155: 2403-2413.
11. Snoussi EH (1998) Necessary conditions for multistationarity and stable periodicity. J Biol Syst 6: 3-9.
12. Soulé C (2003) Graphic requirements for multistationarity. ComPlexUs 1: 123-133.
13. Thomas R (1981) On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations. Synergetics, vol 9, pp 180-193. Springer, Berlin.