Abstract
This chapter’s aims are to determine the necessary and sufficient criteria for the existence of periodic solutions, patterns of periodic solutions, and the existence of eventually periodic solutions of the first order nonlinear difference equations. We emerge with three examples of first order nonlinear difference equations that exhibit periodic solutions and eventually periodic solutions:
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References
Anisimova, A., Avotina, M., Bula, I., Periodic Orbits of Single Neuron Models with Internal Decay Rate 0 < β ≤ 1. Mathematical Modelling and Analysis 18, (2013), 325–345.
Anisimova, A., Avotina, M., Bula, I., Periodic and Chaotic Orbits of a Neuron Model. Mathematical Modelling and Analysis 20, 30–52 (2015)
W.F. Basener, B.P. Brooks, M.A. Radin, and T. Wiandt, Rat Instigated Human Population Collapse on Easter Island. Journal of Non-Linear Dynamics, Psychology and Life Sciences 12, 3, 227–240 (2008).
W.F. Basener, B.P. Brooks, M.A. Radin, and T. Wiandt, Dynamics of a Population Model for Extinction and Sustainability in Ancient Civilizations. Journal of Non-Linear Dynamics, Psychology and Life Sciences 12, 1, 29–54 (2008).
Bula, I., Radin, M.A., Wilkins, N., Neuron model with a period three internal decay rate. Electronic Journal of Qualitative Theory of Differential Equations (EJQTDE); (46), 1–19 (2017).
Bula, I., Radin, M.A., Periodic orbits of a neuron model with periodic internal decay rate. Applied Mathematics and Computation (266), 293–303 (2015).
Zhou, Z., Wu, J., Stable Periodic Orbits in Nonlinear Discrete-Time Neural Networks with Delayed Feedback. Computers and Mathematics with Applications 45, 935–942 (2003)
Yuan, Z., Huang, L., All solutions of a class of discrete-time systems are eventually periodic. Applied Mathematics and Computation 158, 537–546 (2004)
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Radin, M.A. (2018). Periodic Character of Solutions of First Order Nonlinear Difference Equations. In: Periodic Character and Patterns of Recursive Sequences. Springer, Cham. https://doi.org/10.1007/978-3-030-01780-4_3
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DOI: https://doi.org/10.1007/978-3-030-01780-4_3
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-01780-4
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