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. 2018 Jul 24;10:25. doi: 10.3389/fnsyn.2018.00025

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Copyright © 2018 Ozcan and Ozcan.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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Ricker maps for Equation (1). (A) Time series evolution of the Ricker population equation for different values of r (small growth rate). The carrying capacity is set constant at 500 for all cases. The black curve with r = 1 shows an initial exponential increase that stabilizes at the carrying capacity. At r = 2, the population oscillates between two values but stays stable. At r = 3.5, we see chaotic oscillations in the population that shows dramatically high numbers as well as extinction. (B) The bifurcation map which shows the population as r is varied. The period doubling bifurcations lead to chaotic dynamics at about r = 2.7.