Hindmarsh-Rose neuronal model; Hindmarsh-Rose neurons; Input-output approach; Input/output; Neuronal synchronization; Robust synchronization; Control and Systems Engineering; Modeling and Simulation; Control and Optimization
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Franci, Alessio ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Brain-Inspired Computing ; Univ. Paris Sud 11, L2S - Supélec, 91142, Gifsur-Yvette, France
Scardovi, Luca; Department of Electrical Engineering and Information Technology, Technische Universität München (TUM), Munich, Germany
Chaillet, Antoine; Univ. Paris Sud 11, L2S - Supélec, 91142, Gifsur-Yvette, France
Language :
English
Title :
An input-output approach to the robust synchronization of dynamical systems with an application to the Hindmarsh-Rose neuronal model
Publication date :
2011
Event name :
IEEE Conference on Decision and Control and European Control Conference
Event place :
Usa
Event date :
12-12-2011 => 15-12-2011
Main work title :
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Publisher :
Institute of Electrical and Electronics Engineers Inc.
M. Arcak and E. D. Sontag. A passivity-based stability criterion for a class of biochemical reaction networks. Mathematical biosciences and engineering, 5(1):1-19, 2008.
M. Arcak and Eduardo D. Sontag. Diagonal stability of a class of cyclic systems and its connection of the secant criterion. Automatica, 42:1531-1537, 2006.
J. A. Bondy and U. S. R. Murty. Graph theory with applications. 1976.
A. Franci, L. Scardovi, and A. Chaillet. An input-output approach to the robust synchronization of dynamical systems with an application to the Hindmarsh-Rose neuronal model. Preprint. Available at http://hal-supelec. archives-ouvertes.fr/hal-00619169, 2011.
C. Godsil and C. Royle. Algebraic Graph Theory. Springer Graduate Text in Mathematics, 2001.
A. Hamadeh, G. B. Stan, and J. Goncalves. Robust synchronisation in networks of cyclic feedback systems. In Proc. 47th. IEEE Conf. Decision Contr., 2008.
B. Hao, H. Yua, Y. Jinga, and S. Zhanga. On synchronizability and heterogeneity in unweighted networks. Physica A, 338(9):1939-1945, 2009.
J. L. Hindmarsh and R. M. Rose. A model of neuronal bursting using three coupled first-order differential equations. In Proc. Roy. Soc. Lond, volume B 221, pages 87-102, 1984.
A. Holgado, J. Terry, and R. Bogacz. Conditions for the generation of beta oscillations in the subthalamic nucleus-globus pallidus network. J. of Neuroscience, 30(37):12340, 2010.
A. E. Motter, C. Zhou, and J. Kurths. Network synchronization, diffusion, and the paradox of heterogeneity. Phys. Rev. E, 71(1):016116, 2005.
P. Moylan and D. Hill. Stability criteria for large-scale systems. IEEE Trans. on Automat. Contr., 23(2):143-149, 1978.
W. T. Oud and I. Tyukin. Sufficient conditions for synchronization in an ensemble of HINDMARSH AND ROSE neurons: passivity-based approach. IFAC NOLCOS 2004, 2004.
A. Pavlov, A. Pogromsky, N. van de Wouw, and H. Nijmeijer. Convergent dynamics, a tribute to Boris Pavlovich Demidovich. Syst. & Contr. Letters, 52:257-261, 2004.
Q. Pham and J. Slotine. Stable concurrent synchronization in dynamic system networks. Neural Networks, 20(1):62-77, 2007.
J. E. Rubin. Burst synchronization. Scholarpedia, 2(10), 2007.
F. Sato, M. Parent, M. Levesque, and A. Parent. Axonal branching pattern of neurons of the subthalamic nucleus in primates. J Comp Neurol, 424(1):142-152, 2000.
L. Scardovi, M. Arcak, and E. D. Sontag. Synchronization of interconnected systems with applications to biochemical networks: an Input-Output approach. IEEE Trans. on Automat. Contr., 55:1367-1379, 2010.
E. D. Sontag. Passivity gains and the "secant condition" for stability. Syst. & Contr. Letters, 55(3):177-183, 2006.
G. B. Stan, A. Hamadeh, R. Sepulchre, and J. Goncalves. Output synchronization in networks of cyclic biochemical oscillators. In Proc. American Control Conference, pages 3973-3978, 2007.
G.B. Stan and R. Sepulchre. Analysis of interconnected oscillators by dissipativity theory. IEEE Trans. on Automat. Contr., 52(2):256-270, 2007.
A. J. van der Schaft. L2-Gain and passivity techniques in nonlinear control. Communications and Control Engineering. Springer Verlag, London, 2nd. edition, 1999.
M. Vidyasagar. Input-Output Analysis of Large Scale Interconnected Systems. Springer Verlag, Berlin, 1981.
C. W. Wu. Algebraic connectivity of directed graphs. Linear and Multilinear Algebra, 53(3):203-223, 2005.
