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Abstract.

This paper is a presentation of neuronal control systems in the terms of the dynamical systems theory, where (1) the controller and its surrounding environment are seen as two co-dependent controlled dynamical systems (2) the behavioral transitions that take place under adaptation processes are analyzed in terms of phase-transitions. We present in the second section a generic method for the construction of multi-population random recurrent neural networks. The third section gives an overview of the various phase transitions that take place under an external forcing signal, or under internal parametric changes. The section 4 presents some applications in the domain of sequence identification and active perception modeling. The section 5 presents some applications in the domain of closed-loop control systems and reinforcement learning.

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References

  • S. Grossberg, Proc. Natl. Acad. Sci. USA 59, 368–371 (1968)

    Article  MATH  ADS  Google Scholar 

  • S. Amari, IEEE Trans. Syst. Man. Cyb. SMC-2, 643–657 (1972)

    Google Scholar 

  • J. Hopfield, Proc. Nat. Acad. Sci. 79, 2554–2558 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  • G.A. Carpenter, S. Grossberg, Comput. Vis. Graph. Image Process. 37, 54–115 (1987)

    Article  Google Scholar 

  • C. Skarda, W. Freeman, Behav. Brain Sci. 10, 161–195 (1987)

    Google Scholar 

  • M.A. Cohen, S. Grossberg, IEEE Trans. Syst. Man. Cybern. SMC13, 815–826 (1983)

    Google Scholar 

  • S. Amari, IEEE Trans. Comp. C-21, 1197–1206 (1972)

    Google Scholar 

  • H. Sompolinsky, I. Kanter, Phys. Rev. Lett. USA 57, 2861–2864 (1986)

    Article  ADS  Google Scholar 

  • S. Dehaene, J.-P. Changeux, J.-P. Nadal, Proc. Natl. Acad. Sci. USA 84, 2727–2731 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  • F. Delcomyn, Science 210, 492–498 (1980)

    Article  ADS  Google Scholar 

  • P. Meyrand, J. Simmers, M. Moulins, Nature 351, 60–63 (1991)

    Article  ADS  Google Scholar 

  • R. Rao, T. Sejnowski, Neural Comput. 13, 2221–2237 (2001)

    Article  MATH  Google Scholar 

  • C. Leibold, R. Kempter, Neural Comput. 18, 904–941 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • E. Rodriguez, N. George, J.-P. Lachaux, J. Martinerie, B. Renault, F. Varela, Nature 397, 430–433 (1999)

    Article  ADS  Google Scholar 

  • B. Ans, Y. Coiton, J.-C. Gilhodes, J.-L. Velay, Neural Netwo. 7, 1461–1476 (1994)

    Article  Google Scholar 

  • E. Bicho, G. Schöner, Robot. Auton. Syst. 21, 23–35 (1997)

    Article  Google Scholar 

  • S. Haykin, Neural Networks: A Comprehensive Fundation (Prentice-Hall, 1999)

  • G. Dreyfus, J.-M. Martinez, M. Samuelides, M.B. Gordon, F. Badran, S. Thiria, L. Hérault, Réseaux de neurones - Méthodologie et applications (Eyrolles, Paris, 2002)

  • M. Ghallab, D. Nau, P. Traverso, Automated Planning, Theory and Practice (Elsevier, Morgan-Kaufmann, 2004)

  • J.J. Gibson, The Ecological Approach to Visual Perception (Houghton-Mifflin, Boston, 1979)

  • R. Brooks, Artific. Intell. 47, 139–159 (1991)

    Article  Google Scholar 

  • K. O'Regan, G. Noë, Behav. Brain Sci. (2001)

  • R. Sutton, Mach. Learn. 3, 9–44 (1988)

    Google Scholar 

  • K. Doya, Neural Comput. 12, 219–245 (2000)

    Article  Google Scholar 

  • C. Watkins, P. Dayan, Mach. Learn. 8, 279–292 (1992)

    MATH  Google Scholar 

  • R.J. Williams, Mach. Learn. 8, 229–256 (1992)

    MATH  Google Scholar 

  • P. Bartlett, J. Baxter, Hebbian synaptic modifications in spiking neurons that learn, School of Information Science and Engineering, Australian National University, Tech. Rep. (1999)

  • H. Tuckwell, Introduction to Theoretical Neurobiology (Cambridge University Press, 1988)

  • A. Herz, B. Sulzer, R. Kuhn, J.L. van Hemmen, Biol. Cybern. 60, 457–467 (1989)

    Article  MATH  Google Scholar 

  • D. Hebb, The Organization of Behavior (Wiley, New York, 1949)

  • G. Turrigiano, K. Leslie, N. Desai, L. Rutherford, S. Nelson, Nature 391, 892–896 (1998)

    Article  ADS  Google Scholar 

  • T.J. Sejnowski, J. Math. Biol. 4, 303–321 (1977)

    Article  Google Scholar 

  • T.V.P. Bliss, T. Lomo, J. Physiol. 232, 331–356 (1973)

    Google Scholar 

  • H. Markram, J. Lubke, M. Frotscher, B. Sakmann, Science 275, 213–215 (1997)

    Article  Google Scholar 

  • G.-Q. Bi, M.-M. Poo, J. Neurosci. 18, 10464–10472 (1998)

    Google Scholar 

  • S. Song, K. Miller, L. Abbott, Nat. Neurosci. 3, 919–926 (2000)

    Article  Google Scholar 

  • H. Sompolinsky, A. Crisanti, H. Sommers, Phys. Rev. Lett. 61, 259–262 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  • B. Cessac, J. Phys. I (France) 5, 409–432 (1995)

    Article  Google Scholar 

  • B. Doyon, B. Cessac, M. Quoy, M. Samuelides, Int. J. Bif. Chaos 3, 279–291 (1993)

    Article  MATH  Google Scholar 

  • S. Grossberg, Biol. Cybern. 23, 121–134, 196–202 (1976)

    Article  MathSciNet  Google Scholar 

  • S. Amari, Biol. Cybern. 27, 77–87 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  • T. Kohonen, Biol. Cybern. 43, 59–69 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  • G. Schöner, M. Dose, C. Engels, Robot. Auton. Syst. 16, 213–245 (1995)

    Article  Google Scholar 

  • S. Moga, P. Gaussier, A neuronal structure for learning by imitation, in Lecture Notes in Artificial Intelligence – European Conference on Artificial Life, edited by D. Floreano, J.-D. Nicoud, F. Mondada (Lausanne, 1999), pp. 314–318

  • S. Funahashi, C.J. Bruce, P.S. Goldman-Rakic, J. Neurophysiol. 61, 331–349 (1989)

    Google Scholar 

  • R. Ben-Yishai, R. Lev Bar-Or, H. Sompolinsky, Proc. Natl. Acad. Sci. USA 92, 3844–3848 (1995)

    Article  ADS  Google Scholar 

  • R. Ben-Yishai, D. Hansel, H. Sompolinsky, J. Comput. Neurosci. 4, 57–79 (1997)

    Article  Google Scholar 

  • D. Hansel, H. Sompolinsky, J. Comput. Neurosci. 3, 7–34 (1996)

    Article  Google Scholar 

  • M. Camperi, X.-J. Wang, J. Comput. Neurosci. 5, 383–405 (1998)

    Article  MATH  Google Scholar 

  • Wang, J. Neurosci. 19, 9587–9603 (1999)

    Google Scholar 

  • A. Compte, N. Brunel, P.S. Goldman-Rakic, X.-J. Wang, Cerebr. Cortex 10, 910–923 (2000)

    Article  Google Scholar 

  • A.D.E. Guillot, Approche Dynamique de la Cognition Artificielle (Lavoisier, 2002)

  • M. Adachi, A. Kazuyuki, Neural Netw. 10, 83–98 (1997)

    Article  Google Scholar 

  • I. Tsuda, Neural Netw. 5, 313–326 (1992)

    Article  MathSciNet  Google Scholar 

  • U. Riedel, R. Kuhn, J. Van Hemmen, Phys. Rev. A 38, 1105–1108 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  • K. Ntzel, J. Kien, K. Bauer, J. Altman, U. Krey, Biol. Cybern. 70, 553–561 (1994)

    Google Scholar 

  • O. Hoshino, Y. Kashimori, T. Kambara, Biol. Cybern. 79, 109–120 (1998)

    Article  MATH  Google Scholar 

  • S. Amari, Kybernetik 14, 201–215 (1974)

    MathSciNet  Google Scholar 

  • W. Gerstner, R. Ritz, L. Van Hemmen, Biol. Cybern. 68, 363–374 (1993)

    Article  MATH  Google Scholar 

  • N. Brunel, V. Hakim, Neural Comput. 11, 1621–1676 (1999)

    Article  Google Scholar 

  • E. Daucé, O. Moynot, O. Pinaud, M. Samuelides, Neural Proc. Lett. 14, 115–126 (2001)

    Article  MATH  Google Scholar 

  • I Ginzburg, H. Sompolinsky, Phys. Rev. E. 50, 3171–3191 (1994)

    Article  ADS  Google Scholar 

  • O. Moynot, M. Samuelides, PTRF 123, 41–75 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • C. Van Vreeswijk, H. Sompolinsky, Neural Comput. 10, 1321–1371 (1998)

    Article  Google Scholar 

  • E. Daucé, O. Moynot, O. Pinaud, M. Samuelides, B. Doyon, Mean field equations reveal synchronization in a 2-populations neural network model, in ESANN 99, edited by M. Verleysen (D-Facto, 1999), pp. 7–12

  • P. Bush, T. Sejnowski, J. Comput. Neurosci. 3, 91–110 (1996)

    Article  Google Scholar 

  • E.M. Izhikevich, IEEE Trans. Neural Netw. 14, 1569–1572 (2003)

    Article  Google Scholar 

  • E. Daucé, M. Quoy, B. Cessac, B. Doyon, M. Samuelides, Neural Networks 11, 521–533 (1998)

    Article  Google Scholar 

  • W. Singer, Time as coding space in neocortical processing: a hypothesis, in Temporal Coding in the Brain, edited by G. Buzsáki (Springer-Verlag, Berlin, Heidelberg, 1994), pp. 51–79

  • N. Brunel, X.-J. Wang, J. Comput. Neurosci. 11, 63–85 (2001)

    Article  Google Scholar 

  • A. Penn, Steps towards a quantitative analysis of individuality and its maintenance: a case study with multi-agent systems, in Fifth German Workshop on Artificial Life: Abstracting and Synthesizing the Principles of Living Systems, edited by D. Polani, J. Kim, T. Martinez (IOS Press, 2002), pp. 125–134

  • J. Tani, Model-based learning for mobile robot navigation from the dynamical system perspective, IEEE Trans. System, Man and Cybern. B 26, 421–436 (1996)

    Article  Google Scholar 

  • B. Kosko, Bidirectional associative memories, IEEE Trans. Systems, Man Cybern. 18, 49–60 (1988)

    Article  MathSciNet  Google Scholar 

  • F. Varela, Principles of Biological Autonomy (North Holland, Amsterdam, 1979)

  • B. Brembs, F. Lorenzetti, F. Reyes, D. Baxter, J. Byrne, Science 296, 1706–1709 (2002)

    Article  ADS  Google Scholar 

  • J. Daphna, Y. Niv, E. Ruppin, Neural Networks 15, 535–547 (2002)

    Article  Google Scholar 

  • E. Daucé, Nat. Comp. 2, 135–157 (2004)

    Article  Google Scholar 

  • E. Daucé, Hebbian reinforcement learning in a modular dynamic network, in Proceedings of the Eighth International Conference on Simulation of Adaptive Behavior (SAB'04) (2004), pp. 305–314

  • B. Cessac, M. Samuelides, Eur. Phys. J. Special Topics 142, 7–88 (2007)

    Google Scholar 

  • M. Samuelides, B. Cessac, Eur. Phys. J. Special Topics 142, 89–122 (2007)

    Google Scholar 

  • L. Perrinet, Eur. Phys. J. Special Topics 142, 163–225 (2007)

    Google Scholar 

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Daucé, E. Learning and control with large dynamic neural networks. Eur. Phys. J. Spec. Top. 142, 123–161 (2007). https://doi.org/10.1140/epjst/e2007-00060-8

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