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Books on the topic 'Nonlinear periodic systems'

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Published: 19 October 2024

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1

Reithmeier, Eduard. Periodic Solutions of Nonlinear Dynamical Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0094521.

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2

Chulaevskiĭ, V. A. Almost periodic operators and related nonlinear integrable systems. Manchester, UK: Manchester University Press, 1989.

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3

Ambrosetti, A. Periodic solutions of singular Lagrangian systems. Boston: Birkhäuser, 1993.

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4

author, Bolle Philippe, ed. Quasi-periodic solutions of nonlinear wave equations in the D-dimensional torus. Berlin: European Mathematical Society, 2020.

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5

Reithmeier, Eduard. Periodic solutions of nonlinear dynamical systems: Numerical computation, stability, bifurcation, and transition to chaos. Berlin: Springer-Verlag, 1991.

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6

P, Walker K., and United States. National Aeronautics and Space Administration., eds. Nonlinear mesomechanics of composites with periodic microstructure: Final report on NASA NAG3-882. [Washington, DC]: National Aeronautics and Space Administration, 1991.

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7

Fiedler, Bernold. Global bifurcation of periodic solutions with symmetry. Berlin: Springer-Verlag, 1988.

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8

Luo, Albert C. J. Periodic Flows to Chaos in Time-delay Systems. Springer, 2016.

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9

Chulaevsky, V. A. Almost Periodic Operators and Related Nonlinear Integrable Systems (Nonlinear Science: Theory & Application). John Wiley & Sons, 1992.

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10

Coti-Zelati, V., and A. Ambrosetti. Periodic Solutions of Singular Lagrangian Systems. Birkhauser Verlag, 2012.

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11

Ambrosetti, A. Periodic Solutions of Singular Lagrangian Systems. Springer, 2013.

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12

Soliton Management in Periodic Systems. Springer, 2005.

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13

Hassan, Ameer. On the periodic and chaotic responses of Duffing's oscillator. 1989.

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14

Reithmeier, Eduard. Periodic Solutions of Nonlinear Dynamical Systems: Numerical Computation, Stability, Bifurcation and Transition to Chaos. Springer London, Limited, 2006.

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15

Huffaker, Ray, Marco Bittelli, and Rodolfo Rosa. Entropy and Surrogate Testing. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782933.003.0005.

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Abstract:
Reconstructing real-world system dynamics from time series data on a single variable is challenging because real-world data often exhibit a highly volatile and irregular appearance potentially driven by several diverse factors. NLTS methods help eliminate less likely drivers of dynamic irregularity. We set a benchmark for regular behavior by investigating how linear systems of ODEs are restricted to exponential and periodic dynamics, and illustrating how irregular behavior can arise if regular linear dynamics are corrupted with noise or shift over time (i.e., nonstationarity). We investigate how data can be pre-processed to control for the noise and nonstationarity potentially camouflaging nonlinear deterministic drivers of observed complexity. We can apply signal-detection methods, such as Singular Spectrum Analysis (SSA), to separate signal from noise in the data, and test the signal for nonstationarity potentially corrected with SSA. SSA measures signal strength which provides a useful initial indicator of whether we should continue searching for endogenous nonlinear drivers of complexity. We begin diagnosing deterministic structure in an isolated signal by attempting to reconstructed a shadow attractor. Finally, we use the classic Lorenz equations to illustrate how a deterministic nonlinear system of ODEs with at least three equations can generate observed irregular dynamics endogenously without aid of exogenous shocks or nonstationary dynamics.
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16

Rigorous Numerics in Dynamics: AMS Short Course, Rigorous Numerics in Dynamics, January 4-5, 2016, Seattle, Washington. American Mathematical Society, 2018.

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