Zheng, "Adaptive robust fuzzy control for a class of uncertain chaotic systems
," Nonlinear dynamics, vol.
Liu, "Parameter estimation for chaotic systems
by particle swarm optimization," Chaos, Solitons and Fractals, vol.
present highly sensitive to initial conditions; that is, they present different chaotic dynamics when the initial conditions are slightly modified.
Adaptive H8 synchronization of unified chaotic systems
The sensitivity to initial conditions means predicting the behaviour of a chaotic system
is difficult, and becomes more difficult over time.
15) Hence, it is possible to consider chaotic systems
as generating rather than destroying order, insofar as a random scattering of initial points in the phase space will end up being in a more ordered rather than less ordered state as they converge on the attractor.
have been proven to be having correlation with cryptography .
The inherent property of robustness of a Fuzzy Logic System (FLS) makes it an efficient forecaster for chaotic systems
Since the seminal work by Carroll Pecora [1,2], a variety of impressive approaches have been proposed for the synchronization for the chaotic systems
such as PC method [1,2], sampled-data feedback synchronization method , OGY method , adaptive design method [6,7], time-delay feedback approach , backstepping design method [9,10], sliding mode control method , active control method , etc.
This means that the two Lorenz chaotic systems
realize the projective synchronization under the controller (10).
According to that, many properties of chaotic systems
such as: ergodicity, sensitivity to initial conditions/system parameters, mixing property, deterministic dynamics and structural complexity can be considered analogous to the confusion, diffusion with small change in plaintext/secret key, diffusion with a small change within one block of the plaintext, deterministic pseudo randomness and algorithmic complexity properties of traditional cryptosystems .
In other calculations, the researchers found that with some basic tweaks in the design, the new class of metamaterials could also model chaotic systems
, such as disordered planetary motions, by inducing chaos in electromagnetic waves.