This paper reports on the synchronization proprieties in bidirectional coupled current modulated vertical cavity surfaceemitting lasers (CMVCSELs) based on the combined model of Danckaert et al.. Regular pulse packages and chaotic behaviors are found in CMVCSEL during the numerical results. The suitable coupling strength leading to high quality of synchronization is determined by numerical analysis. The consequence of the parameter mismatch and the duration of the synchronization process are also highlighted.

In the last few decades, the dynamics of onedimensional chaotic maps have gained the tremendous attention of scientists and scholars due to their remarkable properties such as perioddoubling, chaotic evolution, Lyapunov exponent, etc. The term hyperbolicity, another important property of chaotic maps is used to examine the regular and irregular behavior of the dynamical systems. In this article, we deal with the hyperbolicity and stabilization of fixed states using a superior twostep feedback system. Due to the superiority in the chaotic evolution of onedimensional maps in the superior system we are encouraged to examine the hyperbolicity and stabilization in chaotic maps. The hyperbolic notion, hyperbolicity in periodic states of prime order, stabilization, and the hyperbolic set of the chaotic maps are studied. The numerical, as well as experimental simulations, are carried out, followed by theorems, examples, remarks, functional plots, and bifurcation diagrams.

Offset boosting is an important issue for chaos control due to its broadband property and polarity
control. There are two main approaches to realize offset boosting. One is resort to parameter introducing
where an offset booster realizes attractor boosting. The other one is by the means of periodic function or
absolute value function where a specific initial condition can extract out any selfreproduced or doubled
attractor with different offset. The former also provides a unique window for observing multistability and the
latter gives the direction for constructing desired multistability.

An effective design procedure has been introduced for implementing the fractional order integrator structures with a modified low pass filters (LPFs) and its functionality is verified by realizing a fractionalorder chaotic system. In these applications, the state variables of the fractionalorder Sprott’s Jerk system are emulated by these first order LPFs. Since the discrete device based designs have the hard adjustment features and the circuit complexities; the realizations of these LPFs are carried out with the Field Programmable Analog Arrays (FPAAs), sensitively. Hence, the introduced LPF based method has been applied to the fractional order Sprott’s Jerk systems and these fractionalorder systems, which are built by the several nonlinear functions, have been implemented with a programmable analog device. In this context, the minimum fractionalorders of the Sprott’s Jerk systems are calculated by considering the stability of the fractionalorder nonlinear systems. After that, these systems are simulated by employing the GrünwaldLetnikov (GL) fractional derivative method by using a common fractionalorder. Thus, the stability analyses of the fractionalorder Sprott’s Jerk system are supported by the numerical simulation results. After the numerical simulation stage, the design procedures of the FPAA based implementations of the Sprott’s Jerk systems have been dealt with in detail. Finally, thanks to the introduced firstorder LPF method, the hardware realizations of the Sprott’s Jerk systems have been achieved successfully with a single FPAA device.

Vibrational behavior and structural failure of a metallic beam submitted to simultaneous action of axial load and fire exposure are investigated. Analyses are made at ambient conditions and for two types of fire, ISO 834 fire and parametric fire. Vibrational equation based on heat conduction equation and field equations are constructed and numerically solved to obtain the responses in terms of time histories, bending moment in fire and time to failure against axial load ratio. The heat flux is high enough to affect material properties of the structure and their variation with temperature is taking into account in the mathematical formulation. Results show that heat flux resulting from fire action transforms the buckling problem occurring at room temperature into a bending one. Nonreversible responses and sooner arising of failure are observed for ISO 834 fire even for axial load ratio not able to cause buckling at room temperature. Unlike the case of ISO fire, parametric fire improves reversible deflections within the exposure time and later occurring of failure.

A cascade function is designed by combining two seed maps that resultantly has more parameters, high complexity, randomness, and more unpredictable behavior. In the paper, a cascade fractal function, i.e. cascadePLMS is proposed by considering the phoenix and lambda fractal functions. The constructed cascadePLMS exhibits the required fractal features such as fractional dimension, selfsimilar structure, and covering entire phase space by the data sequence in addition to the chaotic properties. Due to the chaotic behavior, the proposed function is utilized to generate a pseudorandom number sequence in both integer and binary format. This is the result of an extreme scalability feature of a fractal function that can be implemented on a large scale. A sequence generator is designed by performing the linear function operation to the real and imaginary part of a cascadePLMS, cascadePLJS separately, and the iteration number at which the cascadePLJS converges to the fixed point. The performance analysis results show that the given method has a large keyspace, fast key generation speed, high key sensitivity, and strong randomness. Therefore, the scheme can be efficiently used further to design a secure cryptosystem with the ability to withstand various attacks.

In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multistable systems, many attractors coexist so that their basins of attraction might possess fractal or even Wada boundaries in such a way that the prediction becomes more complicated depending on the initial conditions. Chaotic systems typically present fractal basins in phase space. A small uncertainty in the initial conditions gives rise to a certain unpredictability of the final state behavior. The new notion of basin entropy provides a new quantitative way to measure the unpredictability of the final states in basins of attraction. Simple methods from chaos theory can contribute to a better understanding of fundamental questions in physics as well as other scientific disciplines.

In this study, the Michelson–Morley experiment and the result of this experiment (the speed of light appears to be the same in all directions) were explored. Although Lorentz gave a mathematical explanation (Lorentz transformations) for this, he did not explain the decreasing momentum with the internal motion of systems. In relation to this decreasing momentum, Einstein solved the problem mathematically by proposing that the mass of the systems increases with the movement of systems (moving mass). We will study this process in a chronological order below. Our primary purpose in this study is to open a platform for discussion by asking questions about the changes in moving systems, as suggested by Lorentz and Einstein (length contraction and mass increase of the object), and to propose a different relativity model by presenting our suggestions and opinions in relation to these discussions.

Theoretical analysis and microcontroller implementation of linear resistivecapacitive shunted Josephson junction (LRCSJJ) model are investigated in this paper. The rateequations describing the LRCSJJ model has two or no equilibrium points relying on the external direct current (DC). One of the equilibrium points is a stable node and the other one is a saddle node. The hysteresis loop of currentvoltage characteristics increases with the increasing of the capacitance of Josephson junction (JJ). Excitable mode, limit cycle, periodic and chaotic behaviors are found in LRCSJJ model with external alternative current thanks to the two modulation parameters largest Lyapunov exponents (LLE) diagram. LRCSJJ model exhibits two different shapes of chaotic attractors by varying the modulation amplitude. Finally, the existence of chaotic behaviors is confirmed by microcontroller results obtained from the microcontroller implementation of LRCSJJ model.

This study investigates the power systems that involve various numbers of busbars. To prevent the disturbances and instabilities in the power systems, power system stabilizers and various control methods have been used. A hyperchaotic blackout has been created by using an existing hyperchaotic system. Hyperchaotic voltage collapse and hyperchaotic disturbance have been injected to the test systems. The situations of the various power systems are illustrated under proposed hyperchaotic blackout and noise. The stability analysis of the power system has been executed according to the dynamic features of hyperchaos.
