Among the topics are dynamical properties of fractional models, state space methods for fractional controller design, fractional-order controllers for mechatronics and automotive applications, the fractional-order modeling and control of selected physical systems, and new trends in synchronizing fractional-order chaotic systems
. (Ringgold, Inc., Portland, OR)
TRNG based on chaotic systems
have been proposed , .
The purpose of this work is to show that the use of continuous-time chaotic systems
on WOA is useful in some cases instead of chaotic maps.
Therefore, many studies focused on the chaos synchronization of fractional-order chaotic systems
via T-S fuzzy models.
In addition to the original continuous-time chaotic systems
such as Lorenz and Chen systems, discrete-time chaotic systems
or maps have been proposed and studied.
Srinivasan, "FPGA implementation of novel fractional-order chaotic systems
with two equilibriums and no equilibrium and its adaptive sliding mode synchronization," Nonlinear Dynamics, vol.
Nowadays, an in-depth study of connecting the memristors with chaotic systems
has been conducted by many scholars.
As we know that the positive Lyapunov exponent of the chaotic systems
is a critical prerequisite in these applications.
Compared with low-dimensional chaotic systems
, high-dimensional chaotic systems
have more positive Lyapunov exponents and are more complex, thus making it difficult to predict the dynamic characteristics that can effectively solve the degradation problem of low-dimensional chaotic system
The main feature of this system is having uncountable infinite number of stable equilibria, which is significantly different from other reported chaotic systems
are a special case of nonlinear systems which can be categorized as chaotic if the system possesses at least one positive Lyapunov exponent and hyperchaotic if the system possesses two or more positive Lyapunov exponents.
Numerical analysis and methods for simulating fractional order nonlinear system are proposed by Petras  and MATLAB solutions for fractional order chaotic systems
, discussed by Trzaska Zdzislaw .