Abstract
This paper deals with a general theory of synchronization of systems coupled by an incursive connection. For systems with a time shift, the slave or driven system anticipates the values of the master or driver system by a future time period giving rise to an anticipatory synchronization. Some extensions show the possibility to enhance the anticipatory synchronization. An application is shown in the case of a chaotic delayed Pearl-Verhulst system. A slave model is incursively synchronized to the master system, the simulation of which showing an anticipation of the slave system by a time duration equal to the delay. Other anticipations are also simulated.
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Dubois D. M. (2001), Theory of Incursive Synchronization and Application to the Anticipation of a Chaotic Epidemic. International Journal of Computing Anticipatory Systems, Ed. by D. M. Dubois, Publ. by CHAOS, Vol. 10, pp. 3–18. ISSN 1373-5411.
Dubois D.M., G. Resconi (1993), Introduction to Hyperincursion with Applications to Computer Science, Quantum Mechanics and Fractal Processes, CC-AI, vol. 10, NOS 1–2,pp. 109–148.
Dubois D. M. and Sabatier P.h. (1998), Morphogenesis by Diffusive Chaos in Epidemiological Systems, CP437, Computing Anticipatory Systems, CASYS-First International Conference, edited by Daniel M. Dubois, published by The American Institute of Physics, pp. 295–308.
Pyragas K. (1995), Weak and Strong Synchronization of Chaos, Applied Nonlinear Dynamics and Stochastic Systems near the Millennium, AIP Conference Proceedings 411, edited by J. B. Kadkeand A. Bulsara, pp. 63–68.
Voss Henning U. (2000), Anticipating Chaotic Synchronization, Physical Review E, volume 61, number 5, pp. 5115–5119.
Hénon M. (1976) A two-dimensional mapping with a strange attractor, Comm. Math. Phys. (1976) 69–77.
Mandelbrot B. (1983) The Fractal Geometry of Nature. Freeman, San Francisco
May R. M. (1976) Simple mathematical models with very complicated dynamics. Nature 261, 459–467
Pearl R. (1924) Studies in human biology. William and Wilkins, Baltimore
Peitgen H.-O., Jürgens H., Saupe D. (1982) Chaos and Fractals, Springer-Verlag
Verhulst P. F. (1847) Nuov. Mem. Acad. Royale, Bruxelles, 18, 1, 1845 & 20,1
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Dubois, D.M. (2002). Theory of Incursive Synchronization and Anticipatory Computing of Chaos. In: Roy, R., Köppen, M., Ovaska, S., Furuhashi, T., Hoffmann, F. (eds) Soft Computing and Industry. Springer, London. https://doi.org/10.1007/978-1-4471-0123-9_5
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DOI: https://doi.org/10.1007/978-1-4471-0123-9_5
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