Elementary quadratic chaotic flows with no equilibria

Current-Mode Network Structures Dedicated for Simulation of Dynamical Systems with Plane Continuum of Equilibrium

“…Surprisingly, chaotic attractors can also be hidden in the case of the deterministic dynamical systems without equilibrium as shown in Refs. [34][35][36][37][38][39][40]. Even more interesting discoveries are chaotic systems having only a stable¯xed point; for further study, consult Refs.…”

A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis

“…However it is clear now that the existence of a saddle point is not a necessary condition for existence of chaotic solutions. The reason is that recently many new chaotic systems have been proposed without any equilibria [8], with one stable equilibria [9], with a line of equilibria [10,11], with a curve of equilibria [12,13] and with a plane of equilibria [14]. It seems the relation between equilibria and their stable and unstable manifolds is unknown to us.…”

Megastability: Coexistence of a countable infinity of nested attractors in a periodically-forced oscillator with spatially-periodic damping

“…These systems include dynamical systems with no equilibrium points [13][14][15][16][17][18][19][20][21], with only stable equilibria [22][23][24][25][26][27], with curves of equilibria [28][29][30], with surfaces of equilibria [8,9], and with non-hyperbolic equilibria [31,32]. Many of these examples belong to a new category of dynamical systems with hidden attractors [33][34][35][36][37][38][39][40][41][42].…”