Fractional-order (FO) chaotic systems exhibit random sequences of significantly greater complexity when compared to integer-order systems. This feature makes FO chaotic systems more secure against various attacks in image cryptosystems. In this study, the dynamical characteristics of the FO Sprott K chaotic system are thoroughly investigated by phase planes, bifurcation diagrams, and Lyapunov exponential spectrums to be utilized in biometric iris image encryption. It is proven with the numerical studies the Sprott K system demonstrates chaotic behaviour when the order of the system is selected as 0.9. Afterward, the introduced FO Sprott K chaotic system-based biometric iris image encryption design is carried out in the study. According to the results of the statistical and attack analyses of the encryption design, the secure transmission of biometric iris images is successful using the proposed encryption design. Thus, the FO Sprott K chaotic system can be employed effectively in chaos-based encryption applications.

This investigation centers on megastable systems, distinguished by their countable infinite attractors, with a particular emphasis on the Quadratic Megastable Oscillator (QMO). Unlike traditional megastable oscillators reliant on external excitation, our proposed QMO operates autonomously, contributing to its distinctiveness. Through a comprehensive exploration of the QMO, we elucidate various dynamical behaviors, enriching the understanding of its complex system dynamics. In contrast to conventional megastable oscillators, the QMO yields nested types of multiple attractors for diverse initial conditions, elegantly depicted in phase portraits. To gauge the sustainability of chaotic oscillation, we employ influential parameter bifurcation plots, providing a nuanced insight into the system’s dynamical evolution. The complexity of the proposed system is further underscored by its intricate basins of attraction, accommodating an infinite number of coexisting attractors. Exploring trajectory dynamics, we observe that certain initial conditions lead trajectories to distant destinations, evading the influence of local attractors. This behavior underscores the uniqueness of the QMO and highlights its potential applications in scenarios requiring nonlocalized attractor behaviors. Taking a practical turn, the QMO is applied to biometric fingerprint image encryption, demonstrating its efficacy in real-world applications. Rigorous statistical analyses and vulnerability assessments confirm the success of the QMO in providing secure encryption within chaotic system-based frameworks. This research contributes not only to the theoretical understanding of megastable systems but also establishes the QMO as a valuable tool in encryption applications, emphasizing its robustness and versatility in complex dynamical scenarios.

Chaotic and hyper-chaotic systems are used in various engineering applications such as encryption, communication, and artificial intelligence. Also, chaotic systems are widely used in chaos-based random number generator (RNG) designs as chaotic system signals are not periodic and produce different values continuously. Since multi-scroll chaotic systems (MSCSs) produce more than one scroll, the output values can take more different values than chaotic systems. In this study, the effects of different directional values and/or different numbers of scrolls of multi-scroll chaotic systems on chaos-based random number generators' performance are investigated with NIST 800-22 (National Institute of Standards and Technology) and correlation coefficient tests. As a result of the research, it has been concluded that the use of multi-scroll chaotic systems with different directional values and/or different numbers of scrolls does not always have a direct positive effect on the performance of chaos-based random number generators. Thus, it is necessary to use a special pre-process method that will vary according to the multi-scroll chaotic system to be used for chaos-based RNG designs with good performance.

This paper reports on the theoretical analysis and microcontroller implementation of smooth nonlinear resistor–capacitor shunted Josephson junction (SNRCSJJ) circuit. The smooth nonlinear resistor is described by a cosine interference term. The stability of the equilibrium points obtained from the rate equations describing the SNRCSJJ circuit reveals the existence of saddle node and transcritical bifurcation. The hysteresis loop widths of current–voltage curves increase with the increase in the coherence parameter. Periodic behaviors, relaxation behaviors, chaotic behaviors, bistable periodic attractors, and coexisting attractors are found during the numerical analysis by varying the coherence parameter and modulation parameters of alternative current (AC). In order to use both in real engineering applications and for educational purposes, microcontroller-based digital design with graphic LCD (liquid crystal display) of the SNRCSJJ circuit is designed. The digital design results matched the simulation results.

In the paper, we futher consider a fractional-order system from a modified Chua’s circuit system with the smooth degree of 3 proposed by Fu et al. Bifurcation analysis, multistability and coexisting attractors in the the fractional-order modified Chua’s circuit are studied. In addition, microcontroller-based circuit was implemented in real digital engineering applications by using the fractional-order Chua’s circuit with the piecewise-smooth continuous system.

This paper reports on the numerical analysis, control of coexisting attractors and microcontroller-based design of current modulated edge emitting semiconductor laser (CMEESL). The stability of equilibrium points of solitary edge emitting semiconductor laser found is investigated. By varying the amplitude of modulation current density, CMEESL displays periodic behaviors, period-doubling to chaotic behavior, bistability and coexistence between limit cycle and chaotic attractors. The coexistence between chaotic and limit cycle attractors is destroyed and controlled to a desired monostable trajectory by means of the linear augmentation method. In addition, a microcontroller-based circuit is also designed to indicate that CMEESL can be used in real applications. Microcontroller-based circuit outputs and numerical analysis results confirm each other.

By introducing a discrete memristor and periodic sinusoidal functions, a two-dimensional map with coexisting chaos and hyperchaos is constructed. Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map, along with which other regimes of coexistence such as coexisting chaos, quasi-periodic oscillation, and discrete periodic points are also captured. The hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants meanwhile the amplitude can also be controlled in combination with those coexisting attractors. Based on the nonlinear auto-regressive model with exogenous inputs (NARX) for neural network, the dynamics of the memristive map is well predicted, which provides a potential passage in artificial intelligence-based applications.

The analytical and numerical analyses as well as prediction with artificial neural network (ANN) for chaos-based artificial intelligence applications of quantum dot light emitting diode (QDLED) are investigated in this paper. The system of equations describing QDLED has three, or one equilibrium points depending on the capture rate from wetting layer into the dot and the injection current. The stability analysis of the equilibrium points reveals the existence of Pitchfork and Hopf bifurcations. The different dynamical behaviors (including steady state, periodic and chaotic behaviors) found in QDLED are illustrated in two parameters bifurcation diagrams, phase portraits and time series. Finaly, the QDLED system is predicted using ANN for chaos-based artificial intelligence applications.

An amplitude controllable hyperjerk system is constructed for chaos producing by introducing a nonlinear factor of memristor. In this case, the amplitude control is realized from a single coefficient in the memristor. The hyperjerk system has a line of equilibria and also shows extreme multistability indicated by the initial value-associated bifurcation diagram. FPGA-based circuit realization is also given for physical verification. Finally, the proposed memristive hyperjerk system is successfully predicted with artificial neural networks for AI based engineering applications.

Nowadays, hyperchaotic system (HCSs) have been started to be used in engineering applications because they have complex dynamics, randomness, and high sensitivity. For this purpose, HCSs with different features have been introduced in the literature. In this work, a new HCS with a single discontinuous nonlinearity is introduced and analyzed. The proposed system has one saddle focus equilibrium. When the dynamic properties and bifurcation graphics of the system are analyzed, it is determined that the proposed system exhibits the complex phenomenon of multistability. Moreover, analog electronic circuit design of the proposed system is performed with positive second-generation current conveyor. In addition, an encryption circuit is designed to demonstrate that the proposed system can be used in various engineering applications.

Discovering chaotic systems with special features is of interest in the recent years. In this paper we introduce a new class of simple hyperjerk systems with infinitely coexisting chaotic attractors usually termed as megastability. The novelty of the proposed systems is that the systems shows megastability without external excitation which was not the case in most of the existing megastable attractors discussed in the literatures. Various dynamical properties of one of the proposed systems like the stability of equilibrium points, bifurcation and Lyapunov spectrum are discussed. Also, a circuit realization using off-the-shelf components is shown to prove the implementation feasibility of the systems. In addition, microcontroller based embedded design with graphic LCD of obtained new simple hyperjerk megastable oscillators was realized. Thus, the obtained new oscillators can be used both in a variety of real digital applications such as random number generators, encryption, communication and for educational purposes.

In this study, a novel two-parameter, three-dimensional chaotic system is constructed. The system has no linear terms and its equilibrium is a line, so it is a system with hidden attractors. The system is first studied by computation of its bifurcation diagrams and diagram of Lyapunov exponents. Then, the system is applied to two encryption related problems. First, the problem of secure communications is considered, using the symmetric chaos shift keying modulation method. Here, the states of the chaotic system are combined with a binary information signal in order to mask it, safely transmit it through a communication channel, and successfully reconstruct the information at the receiver end. In the second problem, the states of the system are utilized to design a simple rule to generate a bit sequence that possesses random properties, and is thus suitable for encryption related applications. For both applications, simulations are performed through Matlab to verify the soundness of the designs.

In this work, a novel three dimensional chaotic system with is proposed. The system has no linear terms and a line equilibrium, so it belongs to the category of systems with hidden attractors. The system's dynamical behavior is analysed through its bifurcations diagrams and maximum Lyapunov exponent diagram. Then, the system is applied to the problem of secure communications using the Symmetric Chaos Shift Keying modulation method.

An autonomous five-dimensional (5D) system with offset boosting is constructed by modifying the well-known three-dimensional autonomous Liu and Chen system. Equilibrium points of the proposed autonomous 5D system are found and its stability is analyzed. The proposed system includes Hopf bifurcation, periodic attractors, quasi-periodic attractors, a one-scroll chaotic attractor, a double-scroll chaotic attractor, coexisting attractors, the bistability phenomenon, offset boosting with partial amplitude control, reverse period-doubling, and an intermittency route to chaos. Using a field programmable gate array (FPGA), the proposed autonomous 5D system is implemented and the phase portraits are presented to check the numerical simulation results. The chaotic attractors and coexistence of the attractors generated by the FPGA implementation of the proposed system have good qualitative agreement with those found during the numerical simulation. Finally, a sound data encryption and communication system based on the proposed autonomous 5D chaotic system is designed and illustrated through a numerical example.

There are many works on self-excited and hidden attractors. However the relationship between them is less investigated. In this study we present a system which can have both hidden self-excited attractors. Dynamical properties of the chaotic system are studied using the equilibrium points and Eigenvalues analysis, Lyapunov exponents and bifurcation plots. Since fractional order models are more interesting in engineering applications, the fractional order version of the proposed system is derived using Adomian decomposition method. Bifurcation and stability analysis of the fractional order model shows the existence of chaotic oscillations. To demonstrate the engineering importance of the fractional order model, we have designed a digital communication system with SCSK (Symmetric Chaos Shift Keying) modulation method separately for both self-excited attractor and hidden attractor, the bit error rate performance was compared.

In recent decades, chaos theory has been used in different engineering applications of different disciplines. Discrete chaotic maps can be used in encryption applications for digital applications. In this study, firstly, Lozi, Tinkerbell and Barnsley Fern discrete chaotic maps are implemented based on microcontroller. Then, microcontroller based random number generator is implemented by using the three different two-dimensional discrete chaotic maps. The designed random number generator outputs are applied to NIST (National Institute of Standards and Technology) 800-22 and FIPS (Federal Information Processing Standard) tests for randomness validity. The random numbers are successful in all tests.

The dynamical characteristics and its applications to random number generator of a fractal Josephson junction with unharmonic current-phase relation (FJJUCPR) described by a linear resistive-capacitive-inductance shunted junction (LRCLSJ) model are investigated in this paper. The dependence of the equilibrium points of the system to the external current source or the unharmonic current-phase relation (UCPR) parameter is revealed and their stability are analysed. The inclusion of unharmonic current-phase relation in an ideal or a fractal Josephson junction leads to transform the spiking, bursting and relaxations oscillations to an excitable mode. While the inclusion of fractal characteristics in insulating layer of Josephson junction leads to an increase of the amplitude of the spiking, bursting and relaxations oscillations. The numerical simulations results also indicate that FJJUCPR exhibits self-excited chaotic attractors and two different shapes of hidden chaotic attractors. The FJJUCPR is implemented in field programmable gate arrays (FPGA) in order to validate the numerical simulations results. In addition, random number generator design is performed using chaotic signals of the FJJUCPR. The random number generator design results are successful in the NIST SP 800-22 test.

In this paper, a new jerk system is designed. This system can display different characters of equilibrium points according to the value of its parameters. The proposed nonlinear oscillator can have both self-excited and hidden attractors. Dynamical properties of this system are investigated with the help of eigenvalues of equilibria, Lyapunov exponents' spectrum, and bifurcation diagrams. Also, an electronic circuit implementation is carried out to show the feasibility of this system. As an engineering application of this new chaotic jerk system, a chaotic communication system is realized by correlation delay shift keying. When the results of the communication system are examined, the transmitted information signal is successfully obtained in the receiving unit, and its performance efficiency is investigated in the presence of additive white Gaussian noise.

An autonomous passive–active integrators oscillator with anti-parallel diodes is proposed and analysed in this paper. It consists of anti-parallel diodes and two main blocks: A second-order passive RLC integrator and a first-order active RC integrator. The existence of two Hopf bifurcations is established during the stability analysis of the unique equilibrium point. For a suitable choice of the circuit parameters, the proposed oscillator can generate periodic oscillations, one-scroll, bistable chaotic attractors and antimonotonicity. The electronic circuit realization of the proposed oscillator is carried out to confirm results found during the numerical simulations. A good qualitative agreement is illustrated between the numerical simulations and experimental results. In addition, chaos-based encryption application to protect electrocardiogram (ECG) signals for secure transmission of medical information is performed using the proposed oscillator in chaotic regime. The ECG signals are successfully encrypted and the original ECG signal is successfully decrypted from noisy ECG signals.

Chaotic systems (CS) are chosen for secure communication owing to their interesting features. So, various CS and effective synchronization methods are introduced. Sprott’s jerk chaotic system (SJCS) is one of the simplest CS. It consists of only five terms with one nonlinearity. So, the usage of jerk CS in communication reduces the complexity of the system. In this work, sliding mode control (SMC)-based chaos synchronization of SJCS with analog circuit design is implemented for secure chaotic communication. The advantages of this secure chaotic communication application are to use a simple chaotic jerk system and achieve the synchronization with only one state SMC signal. Totally, a cost-effective secure chaotic communication system is obtained. There is no chaotic communication application realized by any jerk chaotic system. Moreover, the SMC method has not been used for the synchronization of a jerk CS. Furthermore, most of the chaotic communication studies are given only as numerical simulations. Unlike the others works, the design of circuit of the chaotic communication system is implemented and tested for real-world applications. In the implemented application, the information signal which is sent from the transmitter unit has been successfully obtained from the receiver unit.