Abstract
Nonlinear dynamics is about systems whose dynamics is ruled by nonlinear algebraic or nonlinear differential equations. In regard to their physical behavior, the relationships between changes in their inputs and the resultant behavior in their outputs are not proportional to one another. This behavior characterizes them as nonlinear systems. A nonlinear system may present chaotic dynamics if its dynamics is on average exponentially sensitive to changes in its initial condition [1]. In this case, although generated by a deterministic system, a chaotic trajectory appears to be complicated and even resembles having random behavior.
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Notes
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References
Alligood, K. T., Sauer, T. D., & Yorke, J. A. (2000). Chaos: An introduction to dynamical systems. New York: Springer.
Kantz, H., & Schreiber, T. (2003). Nonlinear time series analysis (2nd ed.). Cambridge: Cambridge University Press.
Macau, E. E. N., & Grebogi, C. (1999). Driving trajectories in complex systems. Physical Review E, 59, 4062.
Badii, R., & Politi, A. (1999). Complexity: Hierarchical structures and scaling in physics. Cambridge: Cambridge University Press.
Mitchell, M. (2011). Complexity: A guided tour. New York: Oxford University Press.
Bruzón, M. S., Gandarias, M. L., & de la Rosa, R. (2018). An overview of the generalized Gardner equation: Symmetry groups and conservation laws. In E. E. N. Macau (Ed.), From nonlinear dynamics to complex systems: A mathematical modeling approach. New York: Springer.
Gandarias, M. L., Bruzón, M. S., & Rosa, M. (2018). On symmetries and conservations laws for a generalized Fisher-Kolmogorov-Petrovsky-Piskunov equation. In E. E. N. Macau (Ed.), From nonlinear dynamics to complex systems: A mathematical modeling approach. New York: Springer.
Livorati, A. L. P. (2018). Tunable orbits influence in a driven stadium-like billiard. In E. E. N. Macau (Ed.), From nonlinear dynamics to complex systems: A mathematical modeling approach. New York: Springer.
Chimanski, E. V., Martins, C. G. L., Chertovskih, R., Rempel, E. L., Roberto, M., Caldas, I. L., et al. (2018). Intermittency and transport barriers in fluids. In E. E. N. Macau (Ed.), From nonlinear dynamics to complex systems: A mathematical modeling approach. New York: Springer.
Leonel, E. D., & Marques, M. F. (2018). An investigation of the chaotic transient for a boundary crisis in the Fermi-Ulam model. In E. E. N. Macau (Ed.), From nonlinear dynamics to complex systems: A mathematical modeling approach. New York: Springer.
Eisencraft, M., Evangelista, J. V. C., Costa, R. A., Fontes, R. T., Candido, R., Chaves, D. P. B., et al. (2018). New trends in chaos-based communications and signal processing. In E. E. N. Macau (Ed.), From nonlinear dynamics to complex systems: A mathematical modeling approach. New York: Springer.
Ramírez-Ávila, G. M., Kurths, J., Depickère, S., & Deneubourg, J. L. (2018). Modeling fireflies synchronization. In E. E. N. Macau (Ed.), From nonlinear dynamics to complex systems: A mathematical modeling approach. New York: Springer.
Algar, S. D., Stemler, T., & Small, M. (2018). From flocs to flocks. In E. E. N. Macau (Ed.), From nonlinear dynamics to complex systems: A mathematical modeling approach. New York: Springer.
Donner, R. V., Lindner, M., Tupikina, L., & Mokkenthin, N. (2018). Characterizing flows by complex network methods. In E. E. N. Macau (Ed.), From nonlinear dynamics to complex systems: A mathematical modeling approach. New York: Springer.
Rodrigues, F. A. (2018). Network centrality: An introduction. In E. E. N. Macau (Ed.), From nonlinear dynamics to complex systems: A mathematical modeling approach. New York: Springer.
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Macau, E.E.N. (2019). From Nonlinear Dynamics to Complex Systems: Introduction. In: Macau, E. (eds) A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems . Nonlinear Systems and Complexity, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-78512-7_1
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