A random asymmetric temporal model of multi-agent interactions: Dynamical analysis

Physica D: Nonlinear Phenomena

Volumn 181, Issue 1-2, 2003, Pages 102-120

  Emmanouilides, C J ^a   Kasderidis, S ^b   Taylor, J G ^b  

^a ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

^b KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

Coupled map lattices; Multi agent interactions; Nonlinear dynamics; Time delay

Indexed keywords

COMPUTER SIMULATION; NEURAL NETWORKS; SPIN GLASS; STATISTICAL MECHANICS;

DYNAMIC MEAN FIELD APPROACH;

MULTI AGENT SYSTEMS;

EID: 0038009282     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(03)00094-0     Document Type: Article

References (42)

1. R. Kindermann, J.S. Snell, Markov Random Fields and their Applications, Contemporary Mathematics, vol. 1, American Mathematical Society, Providence, RI, 1980.
2. K.H. Fisher, J.A. Hertz, Spin Glasses, Cambridge University Press, Cambridge, 1991.
3. D. Stauffer, A. Aharony, Introduction to Percolation Theory, 2nd ed., Taylor & Francis, London, 1994.
4. Brock W.A., Pathways to randomness in the economy: emergent nonlinearity and chaos in economics and finance. Estudios Economicos. 8(1):1993;3-55.
5. An M.Y., Kiefer N.M., Local externalities and societal adoption of technologies. J. Evol. Econ. 5:1995;103-117.
6. P.A. David, D. Foray, Percolation structures, Markov random fields and the economics of EDI standards diffusion, in: G. Pogorel (Ed.), Global Telecommunications Strategies and Technological Changes, Elsevier, Amsterdam, 1994.
7. W.A. Brock, S.N. Durlauf, Interactions-based models, in: J. Heckman, E. Leamer (Eds.), Handbook of Econometrics, vol. 5, North-Holland, Amsterdam, 2000.
8. Brock W.A., Durlauf S.N., Discrete choice with social interactions. Rev. Econ. Stud. 28:2001;235-260.
9. M. Aoki, New Approaches to Macroeconomic Modeling: Evolutionary Stochastic Dynamics, Multiple Equilibria, and Externalities as Field Effects, Cambridge University Press, New York, 1996.
10. D.J. Amit, Modeling brain function: the world of attractor neural networks, Cambridge University Press, New York, 1994.
11. J. Hertz, A. Krogh, R.G. Palmer, Introduction to the Theory of Neural Computation, Lecture Notes, vol. I, Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley, Redwood City, 1991.
12. Amari S., Characteristics of random nets of analog neuron-like elements. IEEE Trans. Syst. Man Cybern. 2(5):1972;643-657.
13. Amari S., Yoshida K., Kanatani K., A mathematical foundation for statistical neurodynamics. SIAM J. Appl. Math. 33(1):1977;95-124.
14. Sherrington D., Kirkpatrick S., Solvable model of a spin glass. Phys. Rev. Lett. 35:1975;1792-1796.
15. Kirckpatrick S., Sherrington D., Infinite-ranged models of spin-glasses. Phys. Rev. B. 11:1978;4384-4403.
16. Sompolinsky H., Crisanti A., Sommers H.J., Chaos in random neural networks. Phys. Rev. Lett. 61(3):1988;259-262.
17. Crisanti A., Sompolinski H., Dynamics of spin systems with randomly asymmetric bonds: ising spins and Glauber dynamics. Phys. Rev. A. 37(12):1988;4865-4874.
18. Doyon B., Cessac B., Quoy M., Samuelides M., Control of the transition to chaos in neural networks with random connectivity. Int. J. Bifurc. Chaos. 3(2):1993;279-291.
19. Cessac B., Doyon B., Quoy M., Samuelides M., Mean-field equations bifurcation map and route to chaos in discrete-time neural networks. Physica D. 74:1994;24-44.
20. Cessac B., Increase in complexity in random neural networks. J. Phys. I. 5:1995;109-432.
21. Dauce E., Quoy M., Cessac B., Doyon B., Samuelides M., Self-organization and dynamics reduction in recurrent networks: stimulus presentation and learning. Neural Networks. 11:1998;521-533.
22. Manski C.F., Identification of endogenous social effects: the reflection problem. Rev. Econ. Stud. 60:1993;531-542.
23. Iannacone L.R., Bandwagons and the threat of chaos: interpersonal effects revisited. J. Econ. Behav. Org. 11:1989;431-442.
24. J.B. Rosser, From Catastrophe to Chaos: A General Theory of Economic Discontinuities, Kluwer Academic Publishers, Boston, 1991.
25. Geman S., Almost sure stable oscillations in a large system of randomly coupled equations. SIAM J. Appl. Math. 42(4):1982;695-703.
26. C.J. Emmanouilides, A mean field model with social interactions and network effects in technology diffusion, in: Proceedings of the 26th EMAC Conference, Warwick Business School, May 20-23, 1997, pp. 416-436.
27. A. Crisanti, G. Paladin, A. Vulpiani, Products of Random Matrices in Statistical Physics, Springer Series in Solid-State Sciences, vol. 104, Springer, New York, 1993.
28. J.M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics, vol. 20, Springer, Berlin, 1977.
29. N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1992.
30. C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences, 2nd ed., Springer, Berlin, 1985.
31. J. Honerkamp, Stochastic Dynamical Systems: Concepts, Numerical Methods, Data Analysis, VCH, New York, 1994.
32. J.M. Yeomans, Statistical Mechanics of Phase Transitions, Oxford University Press, Oxford, 1992.
33. A. Lasota, M.C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge University Press, Cambridge, 1985.
34. C. Beck, F. Schlogl, Thermodynamics of Chaotic Systems, Cambridge University Press, Cambridge, 1993.
35. Eckmann J.P., Ruelle D., Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57(3):1985;617-656.
36. H.D.I. Abarbanel, Analysis of Observed Chaotic Data, Springer, New York, 1996.
37. W.A. Brock, W.D. Dechert, J. Scheinkmann, A test for independence based on the correlation dimension, SSRI Working Paper No. 8702, University of Wisconsin, Wisconsin, 1987.
38. m,m≥3 Commun. Math. Phys. 64:1978;35-40.
39. Wolf A., Swift J.B., Swinney H.L., Vastano J.A., Determining Lyapunov exponents from a time series. Physica D. 16:1985;285-317.
40. Gensay R., Dechert W.D., An algorithm for the. n Lyapunov exponents of an n -dimensional unknown dynamical system Physica D. 59:1992;142-157.
41. A. Bowman, A. Azzalini, Applied smoothing techniques for data analysis, Oxford University Press, Oxford, 1997.
42. K. Kaneko (Ed.), Theory and Applications of Coupled Map Lattices, Wiley, New York, 1993.