Simple Chaotic flows with One Stable equilibrium

It is widely recognized that mathematically simple systems of nonlinear differential equations can exhibit chaos. With the advent of fast computers, it is now possible to explore the entire parameter space of these systems with the goal of finding parameters that result in some desired characteristics of the system. Recently there has been increasing attention to some unusual examples of such systems such as those having no equilibrium, stable equilibria, or coexisting attractors [Jafari et al., 2013; Wei, 2011a, 2011b; Wang & Chen, 2012, 2013; Wei & Yang, 2010, 2011, 2012; Wang et al., 2012a, 2012b]. Recent research has involved categorizing periodic and chaotic attractors as either self-excited or hidden [Kuznetsov et al., 2010, 2011a, 2011b; Leonov & Kuznetsov, 2011a, 2011b, 2013a, 2013b; Leonov et al., 2011a, 2011b, 2012]. A self-excited attractor has a basin of attraction that is associated with an unstable equilibrium, whereas a hidden attractor has a basin of attraction that does not intersect with small neighborhoods of any equilibrium points. Thus any dissipative chaotic flow with no equilibrium or with only stable equilibria must have a hidden strange attractor. Only a few such examples have been reported in the literature [Jafari et al., 2013; Wei, 2011a, 2011b;