Three-dimensional chaotic autonomous system with only one stable equilibrium: Analysis, circuit design, parameter estimation, control, synchronization and its fractional-order form

Using Modified Intelligent Experimental Design in Parameter Estimation of Chaotic Systems

“…However, direct measurement of parameters in a real system is often difficult. Therefore, estimation of parameters from an observed chaotic scalar time series has become an active area of research [11][12][13][14]. A basic method for achieving this goal involves optimization in which the model parameters are chosen to minimize some cost functions.…”

A fractional-order form of a system with stable equilibria and its synchronization

“…Fractional-order forms of systems without equilibrium were reported in [39-41, 43, 44], while fractional-order forms of systems with an infinite number of equilibrium points were presented in [42,45,46]. Sifeu et al investigated the fractional-order form of a threedimensional chaotic autonomous system with only one stable equilibrium [65]. In order to determine chaos synchronization between such fractional-order systems, some synchronization schemes were constructed as summarized in Table 1.…”

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].…”