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An ARM-FPGA-based interface for implementing nonlinear systems through project-based learning for undergraduate students is presented in this work. This setup has a low cost and can be utilized in courses (post-graduate and under-graduate) related to dynamical systems to show the complex behaviors such as chaos, bi-stability, hidden attractors, etc. It consists of a Python-based program in the ARM processor to control the implementation on the FPGA board. As examples, the physical implementation of Lorenz system, as well as the realization of a hidden chaotic system are given.

In this work, for the first time a macroeconomic model has been emulated using a microcontroller-based device, considering as case study the Greek economic crises of period 2010-2019. With the use of well-known tools from nonlinear theory, such as phase portrait, bifurcation diagram, Poincare map and Lyapunov exponents, interesting phenomena have been revealed. More precisely, the period-doubling route to chaos, crisis phenomena and coexistence of attractors have been presented in detail.

This work considers a modification of the map proposed in Wang et al. (2020), by replacing its fixed term by a squared hyperbolic tangent term. The modified map is studied and is shown to have a plethora of chaos related phenomena, like period doubling route to chaos, crisis, antimonotonicity, and an infinite number of equilibrium points inside a bounded domain. Then, a pseudo-random bit generator is designed from the given map and it is applied to the encryption of medical data. Specifically, an electrophysiological signal is considered. The resulting design is finally implemented on a 32 bit microcontroller.

This work proposes a chaotic text encryption scheme implemented in a microcontroller device. Initially, a chaotic 1D map is proposed and studied through its bifurcation diagrams and Lyapunov exponent diagram. The map showcases a constant chaotic behavior, which makes it suitable for use in encrytption. Based on this map, a pseudo random bit generator is designed. This generator is then used as a source of deterministic randomness, in order to encrypt a text message, using XOR. The complete scheme is then implemented in two microcontroller devices that can each implement the encryption and decryption procedures. This allows the safe transmission of an information text between the two devices, and can be the basis for further experimentation.

Free Space Optical (FSO) communications have increasingly emerged in the last decade because of their unparalleled, inherent advantages like the high data rate communications with minimal costs. However, the performance of FSO communications systems is severely limited due to numerous agents. One of the deteriorating contributors is the scintillation effect due to atmospheric turbulence, causing rapid fluctuations of the receiving signal’s intensity. Turbulence strength depends on the current weather conditions and can be estimated from many available statistical models proposed. Also, time jitter is another deteriorating contributor, which causes additional impairments to the link’s throughput due to an either early or late misdetection of the received optical pulse’s center. Especially inevitable, time jitter affects high data rate communications, where the corresponding detector’s time slot is quite short. One hopeful FSO performance improvement solution employs the receiver’s diversity technique. In this work new mathematical expressions for the estimation of the average BER performance of NRZ or RZ OOK FSO links with receivers’ diversity are derived. The strong atmospheric turbulence effect is modeled with K - distribution. In addition, time jitter effect is studied, for the first time to the best of the authors’ knowledge, with the generalized Gaussian distribution. Useful numerical results and interesting conclusion are also listed in this work.

In this work, for the first time, the use of a discrete memristive chaotic system for controlling the motion of a mobile robot is presented. The main goal is to cover as soon as possible a given area with the least number of motion commands. Firstly, the analysis of the proposed system is presented in details. After the selection of the set of parameters and initial conditions, in order for the system to be chaotic, it is applied in a mobile robot’s path planning problem. The simulation results proved that there is a lower limit in the system’s integration step h where its performance is efficient. Also, the same technique was applied in the case of a vacuum cleaning robot. As it is observed from the simulation results the robot managed to cover almost all of the given area in a satisfactory number of motion commands avoiding the collision with the placed obstacles.

This research focuses on the problem of area surveillance, using a UAV with a mounted camera that is controlled chaotically. The chaotic motion of the camera is performed by using the values of a chaotic map, to generate random rotation angles for the camera head, which periodically captures photos of the area to be surveyed. In this way, the position of the camera footprint on the ground is unpredictable, and this makes the surveillance path impossible to predict for an adversary. Thus, this approach allows for increased security when required, since the use of unpredictable agents will make it hard to design infiltration strategies. Simulations are performed for several different scenarios, to evaluate the ground coverage of the chaotic camera, as compared to a camera that constantly looks directly below the UAV.

In this paper, a two-parameter one-dimensional chaotic map with hyperbolic tangent and two nested sinusoidal terms is proposed. The reported map exhibits rich chaotic behavior including such phenomena as the period-doubling route to chaos, crisis, and antimonotonicity appearing. The proposed map is applied for the pseudo-random bit generation and image encryption. To generate bit sequences, a simple rule is used. The generated sequences are verified using NIST statistical tests and cross-correlation analysis. Image encryption is performed using two rounds of shuffling of image pixels and XOR operation. We explicitly show the suitability of the proposed algorithm through histogram, correlation, and entropy analysis for the sample grayscale image.

Chaotic systems are prospective for secure data transfer and processing. Over the past decades, many chaos-based encryption schemes have been proposed. It was shown that such cryptosystems are faster than traditional approaches. In this study, we consider a technique for improving pseudo-random sequence generators based on a binary representation of chaotic sequences calculated using a floating-point data type. We show that we can extract more than 40 bits from the binary representation of each real number and use them as the output of the generator in stream ciphers. Moreover, we show that the features of floating-point calculations lead to pseudo-random properties of the least significant bits of the mantissa of numbers obtained by solving the simple systems of linear and nonlinear differential equations without chaotic behavior as well. The obtained results can be used to reconsider and improve chaos-based cryptographic algorithms.

This work addresses the problem of chaotic path planning, using a memory technique to improve performance. In this application, the dynamics of a chaotic system are utilized to generate a series of navigation commands using a simple rule. These commands are then used by an autonomous robot to explore an area. This navigation strategy can bring overall area coverage, but with numerous revisits to the same cells. Here, a memory technique is applied to limit the chaotic motion to cells with the least number of visits, leading to overall improvement in performance. Numerical simulations are performed to evaluate the path planning strategy.

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.

In this work, the problem of designing an efficient chaotic path planning generator for exploring an area is studied. To achieve so, a Chaotic Random Bit Generator (CRBG) is first constructed. The randomness of the generator was tested and verified by the FIPS statistical package. Then, the proposed CRBG is utilized to produce the chaotic motion commands for an autonomous mobile robot moving in a 2D area, in four or eight different directions. A series of simulations have been performed in Matlab, in order to evaluate the efficiency of the proposed method and the results show that the motion in eight directions gives better results with respect to the coverage rate while also the multiple visits to the same cells have been decreased significantly.

In this work, chaos is experimentally observed from a circuit, in which the nonlinear element is a real memristor. To the best of our knowledge, this is the first nonlinear circuit with a commercially available memristor (KNOWM memristor), which has been implemented in order to experimentally investigate chaos and phenomena related with it, such as a route to chaos via period-doubling, one-scroll and the well-known double-scroll chaotic attractors.

This paper addresses the problem of chaotic path planning for the case of an autonomous mobile robot or an autonomous unmanned arial vehicle (UAV) moving in a 3D environment. The aim is to derive a method to generate a series of chaotic motion commands for a UAV that is tasked to explore a given 3D grid. The objective is to generate an unpredictable motion, that will also give good coverage results relative to the number of motions generated. This work adapts a combination of a modified logistic map and a modulo operator to generate the motion directions. An inverse pheromone memory approach is also considered to improve performance. Simulations are then performed to evaluate the performance of the method.

Radio Frequency (RF) energy harvesting is emerging as a potentially reliable method to replace the costly and, difficult to maintain, source of low-power wireless sensors networks. In this paper, a dual-band RF-to-DC rectifier, that operates at LoRaWAN and GSM-900 cellular communication frequency bands, is presented. The system is composed of an impedance matching circuit, an RF-to-DC rectifier, that converts the ambient RF energy into DC voltage able to feed low power devices, and an output load. The proposed system resonates at two different frequencies of 866 MHz and 937 MHz. Numerical results demonstrate that the overall system exhibits an efficiency of 80% with 4.32 V of output voltage at 0 dBm of input power.

This paper reports the method for constructing multiple coexisting attractors from a chaotic system. First, a new four-dimensional chaotic system with only one equilibrium and two coexisting strange attractors is established. By using bifurcation diagrams and Lyapunov exponents, the dynamical evolution of the new system is presented. Second, a feasible and effective method is applied to construct an infinite number of coexisting attractors from the new system. The core of this method is to batch replicate the attractor of the system in phase space via generating multiple invariant sets and the generation of invariant sets depends on the equilibria, which can be extended by using some simple functions with multiple zeros. Finally, we give some numerical results of the appearance of multiple coexisting attractors in the system with sine and sign functions for demonstrating the effectiveness of the method.

The time delay and fractional-order nonlinear systems have attracted great attention for the synchronization and security of information based on chaotic systems. In this paper, a new robust approach to control a fractional order delayed chaotic system is proposed, with the circuit implementation. Based on the theory of nonlinear predictive control and utilizing fundamental properties of fractional calculus, a new theorem to guarantee the convergence of the chaotic trajectory towards the equilibrium point of fractional order time-delay chaotic systems is developed. Numerical simulations are provided to verify the effectiveness of the design and a circuit implementation is performed to show the feasibility of the proposed approach.

This work proposes a novel hyperjerk system, as a generalization of a hyperjerk system proposed by Dalkiran and Sprott. Initially an analysis of the dynamical behavior of the system is performed. Then, the system is applied to the problem of secure communications. This is done by considering the transmitting signal as an additional state, leading to a rectangular descriptor system, for which an observer is designed, thus achieving synchronization and safe input reconstruction. The design is illustrated through numerical simulations and a microcontroller implementation.

In this work, we propose a new fractional-order form of a discrete-time system based on modified logistic map. Some of the important dynamics of this fractional map including the bifurcation graphs have been studied. In addition, we propose a control law aimed at stabilizing the proposed fractional map. Numerical simulations are also presented to confirm the main findings of the study.

One major research field in autonomous mobile robots is the path planning of vehicles. Many missions require fast and complete coverage of the workspace using an unpredictable trajectory. For the first time, a strategy for a complete and fast scanning of an area using an inverse pheromone method combined with a chaotic pseudo random generator is presented in this work. A program has been written in MATLAB, in which a modified chaotic Logistic map is used in order to create an unpredictable trajectory for fast scanning of the workspace. The results are better with regards to other published works related to the use of chaotic systems for guiding mobile robots due to the fact that the robot does not cover the same area multiple times.

In this paper, we propose some fractional forms of Arnold mappings and study the existence of chaos. Using discrete–time fractional calculus, we show that the general behavior of the proposed fractional maps depends on the fractional order. Numerical results are presented to illustrate the findings.

The problem of secure communication is considered for a chaotic system with hidden attractor, through the observer design approach for descriptor systems. By considering the transmitted signal as an additional state, the nonlinear system is rewritten as a semilinear rectangular descriptor system, for which an observer is constructed. The observer synchronization is feasible under some rank conditions on the system matrices, a common assumption on the nonlinearities and the feasibility of an LMI. The design scheme is showcased through numerical simulations.

This paper presents a robot's path planning method based on finite resistive grids. For this reason an environment with obstacles has been converted into a grid with nodes and edges. In more details, the proposed method is focused on the measurement of the least resistance path between the initial position and the goal position in the grid. A program has been written for finding the least resistance path by solving the resistive grid's circuit problem using the node voltage method. The results has been confirmed by using also the PSPICE showing the effectiveness of the proposed method.

This paper presents the implementation of a device, which is based on a microcontroller, for solving nonlinear chaotic dynamical systems. The greatest advantage of this device is that the user can depict, either on an oscilloscope or a PC, three of the most important tools from nonlinear theory, namely the bifurcation diagram, the phase portrait and the Poincare map. For this reason, this device is suitable for use not only for research purposes but also for educational ones, bringing university students closer to the subjects of microcontroller and chaos theory.

Nowadays, the need of information security has become more prevalent than the past, due to the fact that especially in open networks, there is a potential risk of making sensitive information, such as military orders, medical files and personal data vulnerable to unauthorized interceptions. The development of robust cryptographic schemes is thus essential to the provision of information security. During the last decade an interesting relationship between cryptography and chaos theory has been developed. Consequently, several chaos-based cryptosystems have been put forward. In this context, this work presents a text message encryption device, which is based on a Chaotic Random Number Generator (CRNG). This device is realized with a simple microcontroller board, a small keyboard, a USB port and a LCD display. As a chaotic system, the well-known Chua system is chosen due to its rich dynamical behavior. The proposed CRBG, which is very easily implemented, uses the X-OR function in order to achieve better results concerning the “randomness” of the produced bits sequence. The quality of the produced random number sequences is tested by the FIPS-140-2 statistical suite. The satisfactory results from the use of the aforementioned statistical tests, in regard to other previous works, confirm the feasibility of the proposed text encryption device.

In this paper, the analysis, design and circuit synthesis of a fractional-order form of a chaotic jerk system is presented. The proposed system is one of the simplest member of the jerk system's family, because it has the least number of terms, one of which is the unique nonlinear term of the system. For the first time, the hyperbolic sine term is used as a nonlinear term in this kind of jerk systems, which can be easily realized with two antiparallel diodes. Simulation results by using phase portraits and Lyapunov exponents confirm the expected system's chaotic behavior. Moreover, the electronic circuit for the evaluation of the theoretical model of the proposed fractional-order system is presented.

In this work, the implementation of a chaotic oscillator by using a microcontroller is proposed. The dynamical system, which is used, belongs to the recently new proposed category of dynamical systems with hidden attractors. In more details, the system has an infinite number of equilibrium points which is located on an open hyperbolic sine curve. By programming the microcontroller, the three most useful tools of nonlinear theory, the phase portrait, the Poincare map and the bifurcation diagram can be produced. The comparison of these with the respective simulation results, which are produced by solving the continuous dynamical system with Runge-Kutta, verified the feasibility of the proposed method.

Referring to chaos synchronization, it can be noticed the lack of a general approach enabling any type of synchronization to be achieved. Similarly, there is the lack of a unified method for synchronizing both continuous-time and discrete-time systems via a scalar signal. This paper and the companion one [1] aim to bridge these two gaps by presenting a novel general unified framework to synchronize chaotic systems via a scalar signal. This paper focuses on discrete-time systems, while the companion paper [1] deals with continuous-time systems. Herein, the observer-based synchronization framework exploits a structural condition related to the controllability matrix of the error system in order to achieve any type of dead-beat synchronization (i.e., exact synchronization in finite time) via a scalar synchronizing signal. Examples of different types of synchronization are illustrated, with the aim to show the capabilities of the conceived approach.

Studies relating to chaotic circuits have received considerable attention due to a variety of chaos-based applications in science and engineering. This work deals with a novel simple chaotic generator with a single signum nonlinearity. The proposed chaotic generator is simple with only ten elements and can be realized easily. The behavior of such system is discovered through an implementation of the circuit using off-the-shelf components such as op-amps, resistors and capacitors. Moreover the synchronization of two diffusively coupled circuits is also studied experimentally and obtained results are reported. Because of its chaotic behavior as well as its simplicity, the chaotic circuit can be used in engineering applications and for educational purposes.

In this paper, a new model based on piecewise linear (PWL) functions is proposed and analyzed by considering the well known Pernarowski's mathematical model for an isolated beta cell. Contrary to Pernarowski's model, we replace the original cubic functions with PWL functions with multi-segments in order to obtain bursting electrical activity (BEA) of beta cell. The number of segments depends on the required accuracy to generate bursting. Additionally, an electronic design of the proposed model using voltage operational amplifiers is realized. Several SPICE circuit simulations are carried out to validate the PWL function-based model.

A new 4-D memristive system is presented in this paper. The peculiarity of the model is that it displays a line of equilibrium points and it has hyperchaotic dynamics in a particular range of the parameters space. The behavior of the proposed system is investigated through numerical simulations, by using phase portraits, Lyapunov exponents and Poincare sections. Also, its circuital implementation on SPICE confirmed the memristive system's expected dynamics.