  We propose a new simple three-dimensional continuous autonomous model with
two nonlinear terms and observe the dynamical behavior with respect to system
parameters. This system changes the stability of fixed point via Hopf
bifurcation and then undergoes a cascade of a period-doubling route to chaos.
We analytically derive the first Lyapunov coefficient to investigate the nature
of Hopf bifurcation and also investigate well-separated regions for different
kinds of attractors in two-dimensional parameter space. Next, we introduce a
time-scale ratio parameter and calculate the slow manifold using geometric
singular perturbation theory. Finally, the chaotic state is annihilated by
decreasing the value of the time-scale ratio parameter.
