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1

Grusa, K. U. Mathematical analysis of nonlinear dynamic processes. Harlow: Longman Scientific & Technical, 1988.

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2

Oscillations in planar dynamic systems. Singapore: World Scientific, 1996.

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3

Papageorgiou, Evangelos C. Development of a dynamic model for a UAV. Monterey, Calif: Naval Postgraduate School, 1997.

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4

Murthy, V. R. Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems. [Washington, DC]: National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1994.

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5

Grusa, Karl-Ulrich. Mathematical analysis of nonlinear dynamic processes: An introduction to processes governed by partial differential equations. [Harlow, Essex, England]: Longman Scientific & Technical, 1988.

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6

UNESCO. Working Group on Systems Analysis. Meeting. Lotka-Volterra-approach to cooperation and competition in dynamic systems: Proceedings of the 5th Meeting of UNESCO's Working Group on System Theory held on the Wartburg, Eisenach (GDR), March 5-9, 1984. Berlin: Akademie-Verlag, 1985.

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7

Maurice, Holt, Packard Andrew, and Institute for Computer Applications in Science and Engineering., eds. Simulation of a controlled airfoil with jets. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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8

1941-, Brunner H., Zhao Xiao-Qiang, and Zou Xingfu 1958-, eds. Nonlinear dynamics and evolution equations. Providence, R.I: American Mathematical Society, 2006.

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9

Verhulst, F. Nonlinear differential equations and dynamical systems. Berlin: Springer-Verlag, 1990.

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10

Verhulst, Ferdinand. Nonlinear Differential Equations and Dynamical Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-97149-5.

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11

Verhulst, Ferdinand. Nonlinear Differential Equations and Dynamical Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-61453-8.

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12

Makhankov, Vladimir G., and Oktay K. Pashaev, eds. Nonlinear Evolution Equations and Dynamical Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76172-0.

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13

Carillo, Sandra, and Orlando Ragnisco, eds. Nonlinear Evolution Equations and Dynamical Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-84039-5.

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14

Carillo, Sandra. Nonlinear Evolution Equations and Dynamical Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990.

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15

Verhulst, F. Nonlinear differential equations and dynamical systems. 2nd ed. Berlin: Springer, 1996.

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16

Verhulst, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer-Verlag, 1990.

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17

1955-, Carillo S., Ragnisco O. 1946-, and Workshop on Nonlinear Evolution Equations and Dynamical Systems (5th : 1989 : Orthodoxos Akademnia Krētēs), eds. Nonlinear evolution equations and dynamical systems. Berlin: Springer-Verlag, 1990.

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18

Verhulst, Ferdinand. Nonlinear Differential Equations and Dynamical Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996.

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19

Dinu, Liviu. Mathematical concepts in nonlinear gas dynamics. Burnt Mill, Harlow, Essex, England: Longman Scientific & Technical, 1994.

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20

Carmona, R. Nonlinear stochastic integrators, equations, and flows. New York: Gordon and Breach Science Publishers, 1990.

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21

I, Camacho M., Pacifico M. J, and Takens Floris, eds. Dynamical systems and bifurcation theory. Harlow, Essex, England: Longman Scientific & Technical, 1987.

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22

-H, Steeb W., ed. Nonlinear dynamical systems and Carleman linearization. Singapore: World Scientific, 1991.

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23

McCauley, Joseph L. An introduction to nonlinear dynamics and chaos theory. Stockholm: Royal Swedish Academy of Sciences, 1988.

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24

Differential equations and dynamical systems. 2nd ed. New York: Springer, 1996.

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25

Differential Equations and Dynamical Systems. New York, NY: Springer, 1996.

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26

Differential Equations and Dynamical Systems. 3rd ed. New York, USA: Springer, 2001.

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27

Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1993.

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28

Makhan'kov, V. G. Nonlinear Evolution Equations and Dynamical Systems: Needs '90. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991.

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29

1951-, Lines M., ed. Nonlinear dynamics: A primer. Cambridge: Cambridge University Press, 2001.

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30

1950-, Broer H. W., ed. Nonlinear dynamical systems and chaos. Basel: Birkhäuser, 1996.

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31

Navier-Stokes equations and nonlinear functional analysis. 2nd ed. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 1995.

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32

L, Bona J., Saxton Katarzyna 1949-, and Saxton Ralph 1955-, eds. Nonlinear PDE's, dynamics, and continuum physics: 1998 AMS-IMS-SIAM Joint Summer Research Conference on Nonlinear PDE's, Dynamics, and Continuum Physics, July 19-23, 1998, Mount Holyoke College. Providence, R.I: American Mathematical Society, 2000.

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33

A, Sequeira, and International Conference on Navier-Stokes Equations and Related Nonlinear Problems (3rd : 1994 : Funchal, Madeira Islands), eds. Navier-Stokes equations and related nonlinear problems. New York: Plenum Press, 1995.

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34

Engelbrecht, Jüri. Nonlinear Wave Dynamics: Complexity and Simplicity. Dordrecht: Springer Netherlands, 1997.

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35

1934-, Moss Frank, and McClintock P. V. E, eds. Noise in nonlinear dynamical systems. Cambridge: Cambridge University Press, 1988.

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36

1934-, Moss Frank, and McClintock P. V. E, eds. Noise in nonlinear dynamical systems. Cambridge: Cambridge University Press, 1989.

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37

1962-, Kirkilionis Markus, ed. Trends in nonlinear analysis. Berlin: Springer, 2003.

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38

Liao, Shijun. Homotopy Analysis Method in Nonlinear Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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39

Differential equations and dynamical systems. New York: Springer-Verlag, 1991.

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40

Taniguchi, Masaharu. Nonlinear partial differential equations, dynamical systems and their applications. Kyoto: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2014.

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41

Ding, Tong-Ren. Approaches to the qualitative theory of ordinary differential equations: Dynamical systems and nonlinear oscillations. New Jersey: World Scientific, 2007.

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42

Tenreiro, Machado J. A., Baleanu D. (Dumitru), and SpringerLink (Online service), eds. Dynamical Systems and Methods. New York, NY: Springer Science+Business Media, LLC, 2012.

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43

1939-, Verhulst F., ed. Averaging methods in nonlinear dynamical systems. New York: Springer-Verlag, 1985.

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44

1933-, Day Richard Hollis, and Chen Ping, eds. Nonlinear dynamics and evolutionary economics. New York: Oxford University Press, 1993.

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45

Grusa, K. U., and Karl-Ulrich Grusa. Mathematical Analysis of Nonlinear Dynamic Processes: An Introduction to Processes Governed by Partial Differential Equations (Pitman Research Notes in Mathematics Series). Longman Scientific and Technical, 1989.

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46

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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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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47

Simulation of a controlled airfoil with jets. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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48

Staff, Nihon Sugakkai, Nonlinear Dynamics in Partial Differential Equations (Conference) Staff, Shin-Ichiro Ei, Kyushu Daigaku Staff, and Tetsu Mizumachi. Nonlinear Dynamics in Partial Differential Equations. Mathematical Society of Japan, 2015.

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49

Nonlinear Differential Equations and Dynamical Systems. MDPI, 2021. http://dx.doi.org/10.3390/books978-3-0365-0711-8.

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50

Verhulst, Ferdinand. Nonlinear Differential Equations and Dynamical Systems. Springer, 2012.

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