  In this study, we consider nonlinear interactions between components such as
dark energy, dark, matter and radiation in the Friedman-Robertson-Walker
space-time framework and propose a simple interaction model based on time
evolution of the densities of these components. By using this model we show
that these interactions can be given by Lotka-Volterra equation for suitable
equation of state parameters. We numerically solve these coupling equations and
show that interaction dynamics between dark energy-dark matter-matter or dark
energy-dark matter-matter-radiation has a strange attractor for $0>w_{de}>-1$,
$w_{dm}\ge 0$, $w_{m}\ge 0$ and $w_{r}\ge 0$ values. These strange attractors
with the positive Lyapunov exponent clearly show that chaotic dynamics appears
in time evolution of the densities. These results imply that the time evolution
of the universe is chaotic in the presence of interactions between these
components. The present model may has potential to solve some cosmological
problems such as the singularity, cosmic coincidence, crunch, big rip, horizon,
oscillations, emergence of galaxies, and large scale organization of the
universe. Model also connects between dynamics of the competing species in
biological systems and dynamics of the time evolution of the universe, and
offers a new perspective and a different scenario for the universe evolution
unlike well known popular models.
