Differential equations with multispiral attractors, International Journal of Bifurcation and Chaos, vol.09, issue.06, pp.1009-1039, 1999. ,
Synchronization of Chaos, Encyclopedia of Mathematical Physics, pp.213-226, 2006. ,
DOI : 10.1016/B0-12-512666-2/00105-X
Entrainment between heart rate and weak noninvasive forcing, International Journal of Bifurcation and Chaos, vol.10, issue.10, pp.2339-2348, 2000. ,
Synchronization of cardiorhythm by weak external forcing, Discrete Dynamics in Nature and Society, vol.4, issue.3, pp.201-206, 2000. ,
On Devaney's definition of chaos, Amer. Math. Monthly, vol.99, issue.4, pp.332-334, 1992. ,
Neuronal Oscillations in Cortical Networks, Science, vol.304, issue.5679, pp.1926-1938, 2004. ,
DOI : 10.1126/science.1099745
Sur les courbes d??finies par des ??quations diff??rentielles, Acta Mathematica, vol.24, issue.0, pp.1-88, 1901. ,
DOI : 10.1007/BF02403068
The undecidability of the domino problem, Memoirs of the American Mathematical Society, vol.0, issue.66, p.72, 1966. ,
DOI : 10.1090/memo/0066
On Li-Yorke pairs, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2002, issue.547, pp.51-68, 2002. ,
DOI : 10.1515/crll.2002.053
Experimental demonstration of chaos in a microbial food web, Nature, vol.435, pp.1226-1229, 2005. ,
Asymptotic pairs in positive-entropy systems, Ergodic Theory and Dynamical Systems, vol.22, issue.03, pp.671-686, 2002. ,
DOI : 10.1017/S0143385702000342
A hierarchy of coupled maps, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.12, issue.3, pp.719-731, 2002. ,
DOI : 10.1063/1.1502929
Sinai-Bowen-Ruelle measures for certain H???non maps, Inventiones Mathematicae, vol.287, issue.4, pp.541-576, 1993. ,
DOI : 10.1007/BF01232446
A simple electronic circuit realization of the tent map, Chaos, Solitons & Fractals, vol.42, issue.1, pp.12-16, 2009. ,
DOI : 10.1016/j.chaos.2008.10.037
The double scroll family, IEEE Transactions on Circuits and Systems, vol.33, issue.11 ,
DOI : 10.1109/TCS.1986.1085869
Digital communication with synchronized chaotic lasers, Optics Letters, vol.19, issue.24, pp.2056-2058, 1994. ,
DOI : 10.1364/OL.19.002056
Dynamics towards synchronization in hierarchical networks, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.22, p.41224007, 2008. ,
DOI : 10.1088/1751-8113/41/22/224007
Modélisation, analyse et simulation des réseaux génétiques, Médecine/Science, vol.18, pp.492-502, 2002. ,
Dynamics and Effective Topology Underlying Synchronization in Networks of Cortical Neurons, Journal of Neuroscience, vol.26, issue.33, pp.8465-76, 2006. ,
DOI : 10.1523/JNEUROSCI.1627-06.2006
Addendum: Ergodic theory of chaos and strange attractors, Reviews of Modern Physics, vol.57, issue.4, p.1115, 1985. ,
DOI : 10.1103/RevModPhys.57.1115
Building a cellular switch : more lessons from a good egg, Bioessays, vol.21, issue.10, pp.866-870, 1999. ,
Self-perpetuating states in signal transduction : positive feedback, double-negative feedback and bistability. Current opinion in cell biology, pp.140-148, 2002. ,
GLOBAL SYNCHRONIZATION IN TRANSLATION INVARIANT COUPLED MAP LATTICES, International Journal of Bifurcation and Chaos, vol.18, issue.11, pp.3455-3459, 2008. ,
DOI : 10.1142/S0218127408022494
Construction of a genetic toggle switch in escherichia coli, Nature, issue.6767, pp.403339-403381, 2000. ,
Nonlinear oscillations, dynamical systems , and bifurcations of vector fields, Applied Mathematical Sciences, vol.42 ,
Oscillatory behavior in enzymatic control processes Advances in enzyme regulation, pp.425-428, 1965. ,
Matching Rules and Substitution Tilings, The Annals of Mathematics, vol.147, issue.1, pp.181-223, 1998. ,
DOI : 10.2307/120988
Aperiodic Hierarchical Tilings, Foams and emulsions (Cargèse, pp.481-496, 1997. ,
DOI : 10.1007/978-94-015-9157-7_28
Structural stability of Lorenz attractors, Publications math??matiques de l'IH??S, vol.10, issue.1, pp.59-72, 1979. ,
DOI : 10.1007/BF02684769
Abzweigung einer periodischen Lösung von einer stationären eines Differentialsystems, Ber. Verh. Sächs. Akad. Wiss. Leipzig. Math.-Nat. Kl, vol.95, issue.1, pp.3-22, 1943. ,
Devaney's chaos or 2-scattering implies Li???Yorke's chaos, Topology and its Applications, vol.117, issue.3, pp.259-272, 2002. ,
DOI : 10.1016/S0166-8641(01)00025-6
Comportement chaotique des systèmes déterministes, Applied Mathematical Sciences, 1983. ,
Elementary stability and bifurcation theory. Undergraduate Texts in Mathematics, 1990. ,
Modeling and simulation of genetic regulatory networks by ordinary differential equations, Differential Equations, vol.294, pp.766-769, 2003. ,
Spectral properties and synchronization in coupled map lattices, Physical Review E, vol.65, issue.1, p.16201, 2001. ,
DOI : 10.1103/PhysRevE.65.016201
Theory and applications of coupled map lattices. Nonlinear Science : Theory and Applications, 1993. ,
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Inst. HautesÉtudesHautes´HautesÉtudes Sci. Publ. Math, issue.51, pp.137-173, 1980. ,
Looking beyond the details : a rise in system-oriented approaches in genetics and molecular biology, Current Genetics, vol.41, issue.1, pp.1-10, 2002. ,
Systems biology : A brief overview, Science, vol.295, issue.5560, pp.1662-1664, 2002. ,
obtained by projection, Acta Crystallographica Section A Foundations of Crystallography, vol.40, issue.5, pp.580-587, 1984. ,
DOI : 10.1107/S0108767384001203
A new necessary condition on interaction graphs for multistationarity, Journal of Theoretical Biology, vol.248, issue.4, pp.676-685, 2007. ,
DOI : 10.1016/j.jtbi.2007.06.016
Chemical oscillations, waves, and turbulence, volume 19 of Springer Series in Synergetics, 1984. ,
Synchronization analysis of linearly coupled networks of discrete time systems, Physica D: Nonlinear Phenomena, vol.198, issue.1-2, pp.148-168, 2004. ,
DOI : 10.1016/j.physd.2004.08.024
Incorporating the Formation of a Complex between the PER and TIM Proteins, Journal of Biological Rhythms, vol.380, issue.1, pp.70-87, 1998. ,
DOI : 10.1177/074873098128999934
Deterministic nonperiodic flow, J. Atmos. Sci, vol.20, issue.2, pp.130-141, 1963. ,
Etude des motifs dans les oscillations de la réaction de Bélousov-Zhabotinsky(I) : Existence d'un confineur principal pour un modèle contraint particulier. Les annales de l'Enit, pp.69-98, 1989. ,
Period three implies chaos, Amer. Math. Monthly, vol.82, issue.10, pp.985-992, 1975. ,
The metric entropy of diffeomorphisms. I. Characterization of measures satisfying Pesin's entropy formula, Ann. of Math, vol.122, issue.23, pp.509-539, 1985. ,
The metric entropy of diffeomorphisms. II. Relations between entropy, exponents and dimension, Ann. of Math, vol.122, issue.23, pp.540-574, 1985. ,
Stochastic mechanisms in gene expression, Proceedings of the National Academy of Sciences, vol.94, issue.3, pp.814-819, 1997. ,
DOI : 10.1073/pnas.94.3.814
Diophantine approximation and algebraic numbers, Beyond quasicrystals (Les Houches, pp.3-16, 1994. ,
Horseshoes for mappings of the interval, Bull. Acad. Polon ,
General Conclusions: Teleonomic Mechanisms in Cellular Metabolism, Growth, and Differentiation, Cold Spring Harbor Symposia on Quantitative Biology, vol.26, pp.389-401, 1961. ,
DOI : 10.1016/B978-0-12-460482-7.50044-0
On C1 robust singular transitive sets for three-dimensional flows, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.326, issue.1, pp.81-86, 1998. ,
DOI : 10.1016/S0764-4442(97)82717-6
Phenotypic diversity and chaos in a minimal cell model, Journal of Theoretical Biology, vol.240, issue.3, pp.434-442, 2006. ,
DOI : 10.1016/j.jtbi.2005.10.013
Mathematical biology, Biomathematics, vol.19, 1993. ,
Numerical analysis of a comprehensive model of m-phase control in xenopus oocyte extracts and intact embryos, Journal of cell science, vol.106, issue.4, pp.1153-1168, 1993. ,
The qualitative dynamics of a class of biochemical control circuits, Journal of Mathematical Biology, vol.221, issue.1, pp.53-78, 1976. ,
DOI : 10.1007/BF00307858
Multistability in the lactose utilization network of escherichia coli, Nature, issue.6976, pp.427737-740, 2004. ,
Synchronization in chaotic systems, Phys. Rev. Lett, vol.64, pp.821-824, 1990. ,
Driving systems with chaotic signals, Phys. Rev. A, vol.44, pp.2374-2383, 1991. ,
The interaction graph structure of mass-action reaction networks, Journal of Mathematical Biology, 2011. ,
Desychronization of one-parameter families of stable vector fields, Nonlinearity, vol.19, issue.2, pp.261-276, 2006. ,
DOI : 10.1088/0951-7715/19/2/001
Mathematical comments on basic topics in systems biology Mathematical and computational methods in biology : proceedings CIMPA-UNESCO summer school, 2006. ,
The algorithmic beauty of plants, 1996. ,
DOI : 10.1007/978-1-4613-8476-2
A mathematical model for copper homeostasis in Enterococcus hirae, Mathematical Biosciences, vol.203, issue.2, pp.222-239, 2006. ,
DOI : 10.1016/j.mbs.2006.04.009
Inducing chaos in a gene regulatory network by coupling an oscillating dynamics with a hysteresis-type one, Journal of Mathematical Biology, vol.78, issue.2, 2012. ,
DOI : 10.1007/s00285-013-0703-5
URL : https://hal.archives-ouvertes.fr/hal-00586219
Discrete synchronization of hierarchically organized dynamical systems, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00755688
Synchronization : a universal concept in nonlinear sciences, volume 12 of Cambridge Nonlinear Science Series, 2001. ,
Stable periodicity and negative circuits in differential systems, Journal of Mathematical Biology, vol.1, issue.3, pp.593-600, 2011. ,
DOI : 10.1007/s00285-010-0388-y
URL : https://hal.archives-ouvertes.fr/hal-01242441
Synchronization: From pendulum clocks to chaotic lasers and chemical oscillators, Contemporary Physics, vol.216, issue.5, pp.401-416, 2003. ,
DOI : 10.1103/PhysRevLett.90.088101
A case of the existence of a denumerable set of periodic motions, Sov. Math. Dokl, vol.6, pp.163-166, 1965. ,
Diffeomorphisms with Many Periodic Points, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), pp.63-80 ,
DOI : 10.1515/9781400874842-006
Oscillations in notch signaling regulate maintenance of neural progenitors, International Journal of Developmental Neuroscience, vol.26, issue.8, p.58, 2008. ,
DOI : 10.1016/j.ijdevneu.2008.09.140
Graphic Requirements for Multistationarity, Complexus, vol.1, issue.3, pp.123-133, 2003. ,
DOI : 10.1159/000076100
Sniffers, buzzers, toggles and blinkers : dynamics of regulatory and signaling pathways in the cell, Current Opinion in Cell Biology, vol.15, issue.2, pp.221-231, 2003. ,
Biological Feedback, 1990. ,
URL : https://hal.archives-ouvertes.fr/hal-00087681
On the Relation Between the Logical Structure of Systems and Their Ability to Generate Multiple Steady States or Sustained Oscillations, pp.180-193, 1981. ,
DOI : 10.1007/978-3-642-81703-8_24
DETERMINISTIC CHAOS SEEN IN TERMS OF FEEDBACK CIRCUITS: ANALYSIS, SYNTHESIS, "LABYRINTH CHAOS", International Journal of Bifurcation and Chaos, vol.09, issue.10, pp.1889-1905, 1999. ,
DOI : 10.1142/S0218127499001383
About some theorems by L. P. ? Sil nikov ,
Master-slave synchronization from the point of view of global dynamics, Chaos, vol.40, issue.54, pp.441-461693, 1984. ,
Systems of differential equations containing small parameters in the derivatives, Mat. Sbornik N. S, vol.31, issue.73, pp.575-586, 1952. ,
On the existence of oscillatory solutions in negative feedback cellular control processes, Journal of Mathematical Biology, vol.9, issue.4, pp.311-315, 1975. ,
DOI : 10.1007/BF00279849
What???s new on lorenz strange attractors?, The Mathematical Intelligencer, vol.50, issue.1, pp.6-19, 2000. ,
DOI : 10.1007/BF03025276
Global bifurcations and chaos Analytical methods, Applied Mathematical Sciences, vol.73, 1988. ,
Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers, Phys. Rev. Lett, vol.65, pp.1575-1578, 1990. ,
Synchronization in networks of nonlinear dynamical systems coupled via a directed graph, Nonlinearity, vol.18, issue.3, 2005. ,
DOI : 10.1088/0951-7715/18/3/007
What are SRB measures, and which dynamical systems have them ?, Journal of Statistical Physics, vol.108, issue.5/6, pp.733-754, 2002. ,
DOI : 10.1023/A:1019762724717