A 5-D hyperchaotic Rikitake dynamo system with hidden attractors

This paper presents a 5-D hyperchaotic Rikitake dynamo system with three positive Lyapunov exponents which is derived by adding two state feedback controls to the famous 3-D Rikitake two-disk dynamo system. It is noted that the proposed hyperchaotic system has no equilibrium points and hence it exhibits hidden attractors. In addition, the qualitative properties, as well as the adaptive synchronization of the hyperchaotic Rikitake dynamo system with unknown system parameters, are discussed in details. The main results are proved using Lyapunov stability theory and numerical simulations are shown using MATLAB. Moreover, an electronic circuit realization in SPICE has been detailed to confirm the feasibility of the theoretical 5-D hyperchaotic Rikitake dynamo model

FSO links with diversity pointing errors and temporal broadening of the pulses over weak to strong atmospheric turbulence channels

Free space optical (FSO) communication systems show a growing evolution in the commercial and the research field, due to the huge information capacity they provide along with the unlicensed and secure data transmission they can support. However, several destructive effects, such as the atmospheric turbulence and attenuation, the longitudinal pulse broadening due to the time dispersion, the spatial jitter which caused by the pointing errors between the trans-receivers, among others, mitigate their performance characteristics. Thus, for the improvement of the FSO communication systems' performance, many techniques have been proposed, studied and used. In this work, we present a performance study and we derive closed form mathematical expressions for the estimation of the probability of fade for On-Off keying FSO communication systems which use Gaussian longitudinal pulses as information bit carriers, with reception diversity, over gamma gamma or gamma modelled, atmospheric turbulence channels taking into account the pointing errors and the group velocity dispersion (GVD) effect which, affects significantly the systems performance characteristics, especially for long link lengths and high data rate transmission. Finally, the derived mathematical expressions are used in order to present performance results, using common parameter values for channel's and systems' characteristics. © 2015 Elsevier GmbH. All rights reserved. All rights reserved

A Dream that has Come True: Chaos from a Nonlinear Circuit with a Real Memristor

In the last decade, researchers, who work in the field of nonlinear circuits, have the "dream"to use a real memristor, which is the only nonlinear fundamental circuit element, in a new or other reported nonlinear circuit in literature, in order to experimentally investigate chaos. With this intention, for the first time, a well-known nonlinear circuit, in which its nonlinear element has been replaced with a commercially available memristor (KNOWM memristor), is presented in this work. Interesting phenomena concerning chaos theory, such as period-doubling route to chaos, coexisting attractors, one-scroll and double-scroll chaotic attractors are experimentally observed. © 2020 World Scientific Publishing Company

Hidden attractors in a chaotic system with an exponential nonlinear term

Studying systems with hidden attractors is new attractive research direction because of its practical and threoretical importance. A novel system with an exponential nonlinear term, which can exhibit hidden attractors, is proposed in this work. Although new system possesses no equilibrium points, it displays rich dynamical behaviors, like chaos. By calculating Lyapunov exponents and bifurcation diagram, the dynamical behaviors of such system are discovered. Moreover, two important features of a chaotic system, the possibility of synchronization and the feasibility of the theoretical model, are also presented by introducing an adaptive synchronization scheme and designing a digital hardware platform–based emulator

Underwater optical wireless communications with chromatic dispersion and time jitter

The obsolete communication systems used in the underwater environment necessitates the development and use of modern telecommunications technologies. One such technology is the optical wireless communications, which can provide very high data rates, almost infinite bandwidth and very high transmission speed for real time fast and secure underwater links. However, the composition and the optical density of seawater hinder the communication between transmitter and receiver, while many significant effects strongly mitigate the underwater optical wireless communication (UOWC) systems' performance. In this work, the influences of chromatic dispersion and time jitter are investigated. Chromatic dispersion causes the temporal broadening or narrowing of the pulse, while time jitter complicates the detection process at the receiver. Thus, the broadening of the optical pulse due to chromatic dispersion is studied and the influence of the initial chirp is examined. Moreover, the effect of the time jitter is also taken into consideration and for the first time, to the best of our knowledge, a mathematical expression for the probability of fade is extracted, taking into account the influence of both of the above-mentioned effects for a UOWC system. Finally, the appropriate numerical results are presented. © 2019 by the authors

Analysis, synchronization and circuit design of a 4D hyperchaotic hyperjerk system

In this work, a 4D hyperchaotic hyperjerk system, with better results for its Lyapunov exponents and Kaplan-Yorke dimension regarding other systems of this family, as well as its circuit implementation, is presented. Hyperchaotic hyperjerk systems depict complex dynamical behavior in a high-dimensional phase space with n ≥ 4, offering robustness against many types of attacks in private communications. For this reason, an adaptive controller in order to achieve global chaos synchronization of coupled 4D hyperchaotic hyperjerk systems with unknown parameters is designed. The adaptive results in this work are proved using Lyapunov stability theory and the effectiveness of the proposed synchronization scheme is confirmed through the simulation results. © 2018 by the authors

Synchronization phenomena in coupled non-identical chaotic circuits

The last decades, the synchronization between coupled chaotic circuits has attracted the interest of the research community because it is a rich and multi-disciplinary phenomenon with broad range applications, such as in broadband communication systems, in secure communications and in cryptography. For this reason many coupling schemes between identical nonlinear circuits with chaotic behavior have been presented. However, the basic drawback of the majority of these schemes is the request the coupled circuits to be identical, due to the fact that in real world applications this is impossible. Motivated by the aforementioned inevitable feature of this class of circuits, which drives the systems out of synchronization, a unidirectional coupling scheme between non-identical, nonlinear circuits, is presented in this work. The circuit, which is used, realizes a four-dimensional modified Lorenz system, which is capable of producing chaotic and hyperchaotic attractors. Furthermore, the coupling scheme is designed by using Nonlinear Open Loop Controllers to target the synchronization state. The stability of synchronization is ensured by using Lyapunov function stability theory. Simulation results of the proposed coupling scheme by using SPICE are also presented to verify the feasibility of the proposed coupling scheme. © 2016 Eastern Macedonia and Thrace Institute of Technology. All rights reserved

Multi-hop DF relayed FSO links with various modulation formats emulated by a dual-hop scheme for strong turbulence conditions

In this work, we try to minimize the mathematical complexity in analyzing outage and error performance by emulating multi-hop terrestrial FSO communication system as a single dual-hop scheme. More specifically, we approximate the topology of such a system and we estimate analytically its performance, by taking into account various modulation formats for strong and saturated atmospheric turbulence conditions. The theoretical study of the FSO system performance is performed using either the negative exponential or the K distribution models, while the well-known modulation formats on-off keying (OOK), pulse amplitude modulation (PAM) and pulse position modulation (PPM), have been employed. Thus, closed form mathematical expressions for outage probability and average BER estimation are derived and their outcomes can easily be used for the design of modern optical wireless links. Finally, using the obtained mathematical forms, the corresponding numerical results are presented using realistic FSO parameter values. © 2020 Elsevier Gmb

Serially DF relayed hybrid FSO/MMW links with Weibull fading, M-turbulence and pointing errors

The significance of the multiple advantages of the terrestrial FSO links decreases due to fact that their performance depends strongly on the atmospheric conditions. A commonly used way to counterbalance the effects of such phenomena is the employment of hybrid systems, which are using both the optical wireless technology and the millimeter waves as well. Although the use of hybrid technology increases the performance characteristics of the links, the effective link length cannot be extended. This can be done, by using the appropriate scheme with relay nodes. Thus, in this work, a wireless link which consists on multiple selection combining hybrid FSO/MMW subsystems serially connected through DF relays, is studied. In each subsystem, the optical beam of the terrestrial FSO link is assumed to propagate through M(alaga) modeled turbulence with spatial jitter while the MMW channel is assumed to follow Weibull fading statistics. For the whole hybrid FSO/MMW system under consideration, novel accurate performance expressions are derived and numerical results for realistic practical cases are derived. The novelty of this work is that it is the first time, to the best of our knowledge, that this configuration with the specific turbulence, spatial jitter and fading characteristics, is proposed and investigated simultaneously in both directions, i.e. in one hand to increase the performance characteristics of the optical link, using the hybrid technique, and on the other hand, to improve the effective link length, using the relay scheme. © 2020 Elsevier Gmb

Implementation of a laboratory-based educational tool for teaching nonlinear circuits and chaos

The last three decades the subject of nonlinear circuits has become an interesting topic not only due to its applications in various fields but also for educational aims. In this direction, Chua’s circuit is considered a cornerstone because it is a unique platform both for the understanding of nonlinear phenomena and the study of experimental chaos as well. So, in this chapter, a new laboratory setup of Chua’s oscillator circuit is presented. The proposed realization is suitable for studying, in the laboratory, the design of a nonlinear circuit step by step. It is also a very useful tool for illustrating in the oscilloscope well-known phenomena related with chaos theory, such as period doubling route to chaos, crisis phenomena, intermittency, and attractors’ coexistence. The proposed platform could be a useful laboratory-based educational tool for teaching nonlinear circuits in courses related with nonlinear dynamics and chaos for undergraduate, postgraduate and Ph.D. students. © Springer International Publishing Switzerland 2016