Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi–Sugeno (T–S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.

When a new chaotic oscillator is introduced, it must accomplish characteristics like guaranteeing the existence of a positive Lyapunov exponent and a high Kaplan–Yorke dimension. In some cases, the coefficients of a mathematical model can be varied to increase the values of those characteristics but it is not a trivial task because a very huge number of combinations arise and the required computing time can be unreachable. In this manner, we introduced the optimization of the Kaplan–Yorke dimension of chaotic oscillators by applying metaheuristics, e.g., differential evolution (DE) and particle swarm optimization (PSO) algorithms. We showed the equilibrium points and eigenvalues of three chaotic oscillators that are simulated applying ODE45, and the Kaplan–Yorke dimension was evaluated by Wolf’s method. The chaotic time series of the state variables associated to the highest Kaplan–Yorke dimension provided by DE and PSO are used to encrypt a color image to demonstrate that they are useful in implementing a secure chaotic communication system. Finally, the very low correlation between the chaotic channel and the original color image confirmed the usefulness of optimizing Kaplan–Yorke dimension for cryptographic applications.

Libyan Desert Glass (LDG) is a natural silica-rich melted rock found as pieces scattered over the sand and bedrock of the Western Desert of Egypt, northeast of the Gilf Kebir. In this work, a population mixture analysis serves to relate the present spatial distribution of LDG mass density with the Late Oligocene–Early Miocene fluvial dynamics in the Western Desert of Egypt. This was verified from a spatial distribution model that was predicted from the log-normal kriging method using the LDG–mass-dependent transformed variable, Y(x). Both low- and high-density normal populations (–9.2 < Y(x) < –3.5 and –3.8 < Y(x) < 2.1, respectively) were identified. The low-density population was the result of an ordinary fluvial LDG transport/deposition sequence that was active from the time of the melting process, and which lasted until the end of activity of the Gilf River. The surface distribution of the high-density population allowed us to restrict the source area of the melting process. We demonstrate the importance of this geostatistical study in unveiling the probable location of the point where the melting of surficial material occurred and the role of the Gilf River in the configuration of the observed strewn field.