Ewww!! Yes that's true of some Darter, pupfish varieties and other fish species too (Filial Cannibalism)! The dynamics of the population with adults cannibalizing on their offspring can be described by the Ricker map, given by the equation:
Figure 1: Bifurcation Diagram (Click to enlarge) -Plot between R and eta. Chaos and bifurcations and period
doubling observed. We observe the 2 point limit cycle is
observed at R value > 7.4
Figure 2: We observe a 4-point limit cycle for values of R > 12.5, see above figure
The second iterate results in a 2-cycle
periodic solution and then later this branches out and a 4-cycle periodic
solution appears. Thus as R passes through a series of bifurcation values the
character of the solution passes through a series of bifurcations, as period
doubling of the periodic solutions.
As R increases through successive
bifurcations, every even periodic solution branches into a double-periodic
solution and this happens when R is such that the eigenvalue of the periodic
solution passes through −1. The distance between bifurcations in R-space also
gets smaller and smaller.
Bifurcation to higher periodic solutions
eventually leads to chaotic behavior: Initially observe the solution oscillates
between two points then it exhibits a 4-period solution then the solutions
become chaotic. Again around a small window of R = 23-25 we see that the
solutions exhibit regular periodic solutions after which they again become
aperiodic/chaotic. So the same sequence of bifurcations get repeated and it is
akin to a fractal, and the periodicity-aperiodicity-periodicity
sequence is also repeated.
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