Abstract:
In this paper, a differential equation with piecewise constant arguments modeling an
early brain tumor growth is considered. The discretization process in the interval t ∈
[n, n+1) leads to two-dimensional discrete dynamical system. By using the Schur–Cohn
criterion, stability conditions of the positive equilibrium point of the system are obtained.
Choosing appropriate bifurcation parameter, the existence of Neimark–Sacker and flip
bifurcations is verified. In addition, the direction and stability of the Neimark–Sacker
and flip bifurcations are determined by using the normal form and center manifold
theory. Finally, the Lyapunov exponents are numerically computed to characterize the
complexity of the dynamical behaviors of the system
