Most familiar examples of low-dimensional chaotic flows occur in systems having one or more saddle points. Such saddle points allow homoclinic and heteroclinic orbits and the prospect of rigorously proving the chaos when the Shilnikov condition is satisfied. Furthermore, such saddle points provide a means for locating any strange attractors by choosing an initial condition on the unstable manifold in the vicinity of the saddle point.

Recent researches by Leonov and Kuznetsov have involved categorizing periodic and chaotic attractors as either self-excited or hidden. A self-excited attractor has a basin of attraction that is associated with an unstable equilibrium, whereas a hidden attractor (HA) has a basin of attraction that does not intersect with small neighborhoods of any equilibrium points. The classical attractors of Lorenz, Rössler, Chen, Sprott (cases B to S), and other widely-known attractors are those excited from unstable equilibria. From a computational point of view this allows one to use a numerical method in which a trajectory started from a point on the unstable manifold in the neighborhood of an unstable equilibrium, reaches an attractor and identifies it. Hidden attractors cannot be found by this method and are important in engineering applications because they allow unexpected and potentially disastrous responses to perturbations in a structure like a bridge or an airplane wing.

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We are invited to write a complete review paper about “dynamical systems hidden attractors”. I am preparing a list of related references. If you are aware of related publications, can you please help me in completing/correcting the following list? I appreciate if you can add some explanations and reasons for your suggestions.

Best Regards,

Sajad

[email protected]

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Mathematical systems:

In [1-29].

Real systems:

In chaotic circuits [30-54], flexible space launch vehicle [55], drilling system [56-58], radiophysical oscillator [59], fluid convection motion [60], Aircraft Flight Control [61], Rikitake system [62], Van der Pol-Duffing oscillator [63], Rabinovich-Fabrikant system [64, 65], Goodwin oscillator [66], Glukhovsky-Dolzhansky system [67], Tigan and Yang systems [68], relay systems [69]

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