N. Kashtan and U. Alon, Spontaneous evolution of modularity and network motifs, Proceedings of the National Academy of Sciences of the United States of America, vol.102, pp.13773-13778, 2005.

J. Liu and J. Ma, Modulation of temporal dynamics of gene transcription by activator potency in the Drosophila embryo, Development, vol.142, issue.21, pp.3781-3790, 2015.

N. Kashtan, E. Noor, and U. Alon, Varying environments can speed up evolution, Proceedings of the National Academy of Sciences, vol.104, pp.13711-13716, 2007.

A. Crombach and P. Hogeweg, Evolution of evolvability in gene regulatory networks, PLoS computational biology, vol.4, 2008.

A. Crombach and P. Hogeweg, Evolution of resource cycling in ecosystems and individuals. BMC evolutionary biology, vol.9, p.122, 2009.

S. F. Gilbert and D. Epel, Ecological Developmental Biology: Integrating Epigenetics, Medicine, and Evolution, 2009.

S. F. Gilbert, Developmental Biology. Sinauer Associates, 2013.

F. Pagès and S. Kerridge, Morphogen gradients: a question of time or concentration?, Trends in Genetics, vol.16, issue.1, pp.40-44, 2000.

H. L. Ashe and J. Briscoe, The interpretation of morphogen gradients, Development, vol.133, issue.3, pp.385-394, 2006.

E. Dessaud, V. Ribes, N. Balaskas, L. L. Yang, A. Pierani et al., Dynamic assignment and maintenance of positional identity in the ventral neural tube by the morphogen sonic hedgehog, PLoS biology, vol.8, issue.6, p.1233, 2010.

T. Gregor, E. F. Wieschaus, A. P. Mcgregor, W. Bialek, and D. W. Tank, Stability and nuclear dynamics of the bicoid morphogen gradient, Cell, vol.130, issue.1, p.17632061, 2007.

S. Y. Shvartsman, M. Coppey, and A. M. Berezhkovskii, Dynamics of maternal morphogen gradients in Drosophila. Current opinion in genetics & development, vol.18, pp.342-347, 2008.

E. Dessaud, L. L. Yang, K. Hill, B. Cox, F. Ulloa et al., Interpretation of the sonic hedgehog morphogen gradient by a temporal adaptation mechanism, Nature, vol.450, pp.717-720, 2007.

E. Kutejova, J. Briscoe, and A. Kicheva, Temporal dynamics of patterning by morphogen gradients. Current opinion in genetics & development, vol.19, pp.315-322, 2009.

G. T. Reeves, N. Trisnadi, T. V. Truong, M. Nahmad, S. Katz et al., Dorsal-ventral gene expression in the Drosophila embryo reflects the dynamics and precision of the dorsal nuclear gradient. Developmental cell, vol.22, pp.544-557, 2012.

N. Balaskas, A. Ribeiro, J. Panovska, E. Dessaud, N. Sasai et al., Gene regulatory logic for reading the Sonic Hedgehog signaling gradient in the vertebrate neural tube, Cell, vol.148, p.22265416, 2012.

A. Kicheva, M. Cohen, and J. Briscoe, Developmental pattern formation: insights from physics and biology, Science, vol.338, issue.6104, p.23066071, 2012.

J. Jaeger, The gap gene network, Cellular and Molecular Life Sciences, vol.68, issue.2, p.20927566, 2011.

J. Reinitz and D. H. Sharp, Mechanism of eve stripe formation, Mechanisms of development, vol.49, issue.1, pp.133-158, 1995.

J. Reinitz, E. Mjolsness, and D. H. Sharp, Model for cooperative control of positional information in Drosophila by bicoid and maternal hunchback, Journal of Experimental Zoology, vol.271, issue.1, pp.47-56, 1995.

E. Mjolsness, D. H. Sharp, and J. Reinitz, A connectionist model of development, Journal of theoretical Biology, vol.152, issue.4, pp.429-453, 1991.

. Manu, S. Surkova, A. V. Spirov, V. V. Gursky, H. Janssens et al., Canalization of gene expression in the Drosophila blastoderm by gap gene cross regulation, PLoS biology, vol.7, issue.3, p.1000049, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00431229

. Manu, S. Surkova, A. V. Spirov, V. V. Gursky, H. Janssens et al., Canalization of gene expression and domain shifts in the Drosophila blastoderm by dynamical attractors, PLoS computational biology, vol.5, issue.3, p.1000303, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00431228

J. Jaeger, M. Blagov, D. Kosman, K. N. Kozlov, E. Myasnikova et al., Dynamical analysis of regulatory interactions in the gap gene system of Drosophila melanogaster, Genetics, vol.167, issue.4, pp.1721-1737, 2004.

J. Jaeger, S. Surkova, M. Blagov, H. Janssens, D. Kosman et al., Dynamic control of positional information in the early Drosophila embryo, Nature, vol.430, issue.6997, pp.368-371, 2004.

M. Ashyraliyev, K. Siggens, H. Janssens, J. Blom, M. Akam et al., Gene circuit analysis of the terminal gap gene huckebein, PLoS Comput Biol, vol.5, issue.10, p.1000696, 2009.

T. J. Perkins, J. Jaeger, J. Reinitz, and L. Glass, Reverse engineering the gap gene network of Drosophila melanogaster, Plos Computational Biology, vol.2, issue.5, p.51, 2006.

P. M. Macdonald and G. Struhl, A molecular gradient in early Drosophila embryos and its role in specifying the body pattern, Nature, vol.324, issue.6097, p.537, 1986.

, Dynamic Gradients Set Timing and Shift-Rates for, Gap Gene Expression PLOS Computational Biology, 2017.

J. Jaeger, D. H. Sharp, and J. Reinitz, Known maternal gradients are not sufficient for the establishment of gap domains in Drosophila melanogaster, Mechanisms of development, vol.124, issue.2, p.17196796, 2007.

H. Wu, R. Jiao, and J. Ma, Temporal and spatial dynamics of scaling-specific features of a gene regulatory network in Drosophila, Nature communications, vol.6, 2015.

H. L. Liang, C. Y. Nien, H. Y. Liu, M. M. Metzstein, N. Kirov et al., The zinc-finger protein Zelda is a key activator of the early zygotic genome in Drosophila, Nature, vol.456, issue.7220, pp.400-403, 2008.

K. R. Wotton, E. Jiménez-guri, A. Crombach, H. Janssens, A. Alcaine-colet et al., Quantitative system drift compensates for altered maternal inputs to the gap gene network of the scuttle fly Megaselia abdita, Elife, vol.4, p.4785, 2015.

A. Crombach, D. Cicin-sain, K. R. Wotton, and J. Jaeger, Medium-throughput processing of whole mount in situ hybridisation experiments into gene expression domains, PLoS One, vol.7, issue.9, p.23029561, 2012.

W. Crombach, . Kr, D. Cicin-sain, M. Ashyraliyev, and J. Jaeger, Efficient reverse-engineering of a developmental gene regulatory network, PLoS Comput Biol, vol.8, issue.7, 2012.

K. Becker, E. Balsa-canto, D. Cicin-sain, A. Hoermann, H. Janssens et al., Reverse-engineering post-transcriptional regulation of gap genes in Drosophila melanogaster, PLoS Computational Biology, vol.9, issue.10, p.1003281, 2013.

S. Strogatz, Nonlinear dynamics and chaos, 1994.

P. François and E. D. Siggia, Phenotypic models of evolution and development: geometry as destiny. Current opinion in genetics and development, vol.22, pp.627-633, 2012.

S. Huang, The molecular and mathematical basis of Waddington's epigenetic landscape: A framework for post-Darwinian biology?, BioEssays, vol.34, p.22102361, 2012.

J. Jaeger and A. Crombach, Life 0 s Attractors. Evolutionary Systems Biology, 2012.

V. V. Gursky, L. Panok, E. M. Myasnikova, M. G. Samsonova, J. Reinitz et al., Mechanisms of gap gene expression canalization in the Drosophila blastoderm, BMC systems biology, vol.5, issue.1, p.118, 2011.

G. Struhl, P. Johnston, and P. A. Lawrence, Control of Drosophila body pattern by the hunchback morphogen gradient, Cell, vol.69, issue.2, pp.237-249, 1992.

S. Surkova, D. Kosman, K. Kozlov, E. Myasnikova, A. A. Samsonova et al., Characterization of the Drosophila segment determination morphome. Developmental biology, vol.313, p.18067886, 2008.

B. Verd, A. Crombach, and J. Jaeger, Classification of transient behaviours in a time-dependent toggle switch model. BMC systems biology, vol.8, p.43, 2014.

B. Verd, E. Clark, K. R. Wotton, H. Janssens, E. Jiménez-guri et al., A damped oscillator imposes temporal order on posterior gap gene expression in Drosophila, Under Review in Proceedings of the National Academy of Sciences, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01934923

J. R. Collier, N. Monk, P. K. Maini, and J. H. Lewis, Pattern formation by lateral inhibition with feedback: a mathematical model of delta-notch intercellular signalling, Journal of Theoretical Biology, vol.183, issue.4, p.9015458, 1996.

A. Pisarev, E. Poustelnikova, M. Samsonova, and R. J. Flyex, the quantitative atlas on segmentation gene expression at cellular resolution, Nucleic acids research, vol.37, pp.560-566, 2009.

K. W. Chu, Y. Deng, and J. Reinitz, Parallel simulated annealing by mixing of states, Journal of Computational Physics, vol.148, issue.2, pp.646-662, 1999.

S. D. Conte and C. De-boor, Elementary Numerical Analysis: An Algorithmic Approach, 1980.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C, vol.2, 1996.

J. Panovska-griffiths, K. M. Page, and J. Briscoe, A gene regulatory motif that generates oscillatory or multiway switch outputs, Journal of The Royal Society Interface, vol.2013, issue.79, p.20120826

A. Crombach, M. A. García-solache, and J. Jaeger, Evolution of early development in dipterans: reverse-engineering the gap gene network in the moth midge Clogmia albipunctata (Psychodidae), Biosystems, vol.123, p.24911671, 2014.

F. Corson and E. D. Siggia, Geometry, epistasis, and developmental patterning, Proceedings of the National Academy of Sciences, vol.109, issue.15, pp.5568-5575, 2012.

A. Crombach, K. R. Wotton, E. Jiménez-guri, and J. Jaeger, Gap gene regulatory dynamics evolve along a genotype network, Molecular biology and evolution, vol.33, issue.5, pp.1293-1307, 2016.

P. E. Kloeden and M. Rasmussen, Nonautonomous Dynamical Systems. Mathematical surveys and monograph, 2011.