Detecting chaos requires careful analysis of periodic data

C. S. Holling. Some characteristics of simple types of predation and parasitism. The Canadian Entomologist, 91(7):385--398, 1959. https://doi.org/10.4039/Ent91385-7

B. W. Kooi, M. P. Boer, and S. A. L. M. Kooijman. On the use of the logistic equation in models of food chain. Bulletin of Mathematical Biology, 60:231--246, 1998. https://doi.org/10.1006/bulm.1997.0016

M. Gyllenberg, I. Hanski, and T. Lindström. A predator-prey model with optimal suppression of reproduction in the prey. Mathematical Biosciences 134: 119--152, 1996. https://doi.org/10.1016/0025-5564(95)00082-8

M. Gyllenberg, I. Hanski, and T. Lindström. Continuous versus discrete single species population models with adjustable reproductive strategies. Bulletin of Mathematical Biology, 59(4):679--705, 1997. https://doi.org/10.1007/BF02458425

J. A. J. Metz and 0. Diekmann. The Dynamics of Physiologically Structured Populations. Springer-Verlag, 1986.

T. Lindström. On the dynamics of discrete food-chains: Low- and high-frequency behavior and chaos. Journal of Mathematical Biology, 45:396--418, 2002. https://doi.org/10.1007/s002850200154

T. Lindström. Dependencies between competition and predation - and their consequences for initial value sensitivity. SIAM Journal of Applied Mathematics, 59(4): 1468--1486, 1999. https://www.jstor.org/stable/118462

R. Devaney. An Introduction to Chaotic Dynamical Systems. Addison-Wesley Publishing Company, Inc, 1989.

A. Lomnicki. Population Ecology of Individuals, volume 25 of Monographs in Population Biology. Princeton University Press, Princeton, New Jersey, 1988.

R. M. May and G. F. Oster. Bifurcations and dynamic complexity in simple ecological models. The American Naturalist, 110(974) :573--599, 1976. https://www.jstor.org/stable/2459579

J. Guckenheimer, G. Oster, and A. Ipaktchi. The dynamics of density dependent population models. Journal of Mathematical Biology, 4: 101 --147, 1977. https://doi.org/10.1007/BF00275980

K. P. Burnham and D. R. Andersson. Model selection and multimodel inference.10 Springer, 2002.

T. J. Hastie and R. J. Tibshirani. Generalized Additive Models. Chapman & Hall, London, 1990.

P. J. Green and B. W. Silverman. Nonparametric regression and Generalized Linear Models, Volume 58 of Monographs on Statistics and Applied Probability. Chapman & Hall, 1994.

H. Akaike. Information theory and an extension of the maximum likelihood principle. In B. N. Petrov and F. Csaki, editors, 2nd International Symposium on Information Theory, pages 267--281. Akademia Kiado, Budapest, 1973.

C. M. Hurvich and C.-L. Tsai. Regression and time series model selection in small samples. Biometrika, 76:297--307, 1989.

T. Lindström and H. Thunberg. An elementary approach to dynamics and bifurcations of skew tent maps. Preprint, 2007. https://doi.org/10.1080/10236190801927462

W. E. Ricker. Stock and recruitment. Journal of the Fisheries Research Board of Canada, 11 (5) :559--623, 1954.

J. H. Friedman. Multivariate adaptive regression splines. The Annals of Statistics 19( 1) : 1 --141, 1991.

M. Lima. The dynamics of natural populations: feedback structures in fluctuating environments. Revis/a chliena de historia natural, 74(2) :317--329, 2001. http://dx.doi.org/10.4067/S0716-078X2001000200009.