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The abilities of quantitative description of noise are restricted due to its origin, and only statistical and spectral analysis methods can be applied, while an exact time evolution cannot be defined or predicted. This emphasizes the challenges faced in many applications, including communication systems, where noise can play, on the one hand, a vital role in impacting the signal-to-noise ratio, but possesses, on the other hand, unique properties such as an infinite entropy (infinite information capacity), an exponentially decaying correlation function, and so on. Despite the deterministic nature of chaotic systems, the predictability of chaotic signals is limited for a short time window, putting them close to random noise. In this article, we propose and experimentally verify an approach to achieve Gaussian-distributed chaotic signals by processing the outputs of chaotic systems. The mathematical criterion on which the main idea of this study is based on is the central limit theorem, which states that the sum of a large number of independent random variables with similar variances approaches a Gaussian distribution. This study involves more than 40 mostly three-dimensional continuous-time chaotic systems (Chua's, Lorenz's, Sprott's, memristor-based, etc.), whose output signals are analyzed according to criteria that encompass the probability density functions of the chaotic signal itself, its envelope, and its phase and statistical and entropy-based metrics such as skewness, kurtosis, and entropy power. We found that two chaotic signals of Chua's and Lorenz's systems exhibited superior performance across the chosen metrics. Furthermore, our focus extended to determining the minimum number of independent chaotic signals necessary to yield a Gaussian-distributed combined signal. Thus, a statistical-characteristic-based algorithm, which includes a series of tests, was developed for a Gaussian-like signal assessment. Following the algorithm, the analytic and experimental results indicate that the sum of at least three non-Gaussian chaotic signals closely approximates a Gaussian distribution. This allows for the generation of reproducible Gaussian-distributed deterministic chaos by modeling simple chaotic systems. [ABSTRACT FROM AUTHOR]

Adaptive oscillators can learn and encode information in dynamic, plastic states. The pendulum has recently been proposed as the base oscillator of an adaptive system. In a mechanical setup, the horizontally forced pendulum adaptive frequency oscillator seeks a resonance condition by modifying the length of the pendulum's rod. This system stores the external forcing frequency when the external amplitude is small, while it can store the resonance frequency, which is affected by the nonlinearity of the pendulum, when the external amplitude is large. Furthermore, for some frequency ranges, the pendulum adaptive frequency oscillator can exhibit chaotic motion when the amplitudes are large. This adaptive oscillator could be used as a smart vibratory energy harvester device, but this chaotic region could degrade its performance by using supplementary energy to modify the rod length. The pendulum adaptive frequency oscillator’s equations of motions are discussed, and a field-programmable analog array is used as an experimental realization of this system as an electronic circuit. Bifurcation diagrams are shown for both the numerical simulations and experiments, while period-3 motion is shown for the numerical simulations. As little work has been done on the stability of adaptive oscillators, the authors believe that this work is the first demonstration of chaos in an adaptive oscillator.

A specific topology of Digital Nonlinear Oscillators (DNOs) has been implemented by using commercial off-the-shelf digital components to experimentally verify and demonstrate the capability of these circuits to support complex dynamics, independently from their implementation technology. In detail, a direct experimental evidence of the DNO dynamical behavior is presented at the analog level with a bifurcation diagram analysis, investigation of periodic and chaotic attractors, and dynamical stability. The autonomous circuit has been investigated as a source of entropy, adopting different figures of merit, including the Lempel–Ziv Complexity, to evaluate the dynamics measured under different operating conditions. [ABSTRACT FROM AUTHOR]

This article mainly studied the transmission synchronization of multiple memristor chaotic circuits by using a single input controller strategy. For transmission synchronization model, the definition of synchronization is established, and based on the stability of minimum phase system, the sufficient conditions of system stability are obtained to ensure that the system error curves of multiple memristor chaotic circuits can maintain asymptotical synchronization. Furthermore, the results of synchronization circuit experiment illustrate that the designed controller works well for the synchronization of multiple memristor chaotic circuits. Finally, the results of secure communication experiment based on transmission synchronization show that the scheme is feasible. • A transmission synchronization scheme is investigated by a single input control method. • The circuit of transmission synchronization is implemented. • An encryption technique illustrates the effectiveness of secure communication. [ABSTRACT FROM AUTHOR]

Adaptive oscillators can learn and encode information in dynamic, plastic states. The pendulum has recently been proposed as the base oscillator of an adaptive system. In a mechanical setup, the horizontally forced pendulum adaptive frequency oscillator seeks a resonance condition by modifying the length of the pendulum's rod. This system stores the external forcing frequency when the external amplitude is small, while it can store the resonance frequency, which is affected by the nonlinearity of the pendulum, when the external amplitude is large. Furthermore, for some frequency ranges, the pendulum adaptive frequency oscillator can exhibit chaotic motion when the amplitudes are large. This adaptive oscillator could be used as a smart vibratory energy harvester device, but this chaotic region could degrade its performance by using supplementary energy to modify the rod length. The pendulum adaptive frequency oscillator's equations of motions are discussed, and a field-programmable analog array is used as an experimental realization of this system as an electronic circuit. Bifurcation diagrams are shown for both the numerical simulations and experiments, while period-3 motion is shown for the numerical simulations. As little work has been done on the stability of adaptive oscillators, the authors believe that this work is the first demonstration of chaos in an adaptive oscillator. [ABSTRACT FROM AUTHOR]

A method for true random number generation by directly sampling a high frequency chaotic jerk circuit is explored. A method for determination of the maximum Lyapunov exponent, and thus the maximum bit rate for true random number generation, of the jerk system of interest is shown. The system is tested over a wide range of sampling parameters in order to simulate possible hardware configurations. The system is then implemented in high speed electronics on a small printed circuit board to verify its performance over the chosen parameters. The resulting circuit is well suited for random number generation due to its high dynamic complexity, long term aperiodicity, and extreme sensitivity to initial conditions. This system passes the Dieharder RNG test suite at 3.125 Mbps.

Compared with the two-valued memristor, the three-valued memristor has higher data density, richer dynamic characteristics, and more potential in digital logic and chaotic circuit. The present model of the three-valued memristor has several limitations. It doesn't perform well enough in three-valued applications since its hysteresis loops are linear and asymmetric. The mathematical model of the three-valued memristor with nonlinear and symmetric hysteresis loops is proposed in this research. To further investigate the electrical characteristics of the three-valued memristor, a circuit emulator of the memristor has been constructed with fundamental components. Multisim simulations and hardware experiments demonstrate the emulator's effectiveness. The three-valued memristor application in chaotic circuits shows fascinating dynamic characteristics and lays the foundation for future research. • The mathematical model of the three-valued memristor with nonlinear and symmetric hysteresis loops is proposed in this paper. • A circuit emulator of the three-valued memristor is proposed and verified using hardware and software. • The three-valued memristor application in chaotic circuits shows fascinating dynamic characteristics. [ABSTRACT FROM AUTHOR]

The spread of epidemics and diseases is known to exhibit chaotic dynamics; a fact confirmed by many developed mathematical models. However, to the best of our knowledge, no attempt to realize any of these chaotic models in analog or digital electronic form has been reported in the literature. In this work, we report on the efficient FPGA implementations of three different virus spreading models and one disease progress model. In particular, the Ebola, Influenza, and COVID-19 virus spreading models in addition to a Cancer disease progress model are first numerically analyzed for parameter sensitivity via bifurcation diagrams. Subsequently and despite the large number of parameters and large number of multiplication (or division) operations, these models are efficiently implemented on FPGA platforms using fixed-point architectures. Detailed FPGA design process, hardware architecture and timing analysis are provided for three of the studied models (Ebola, Influenza, and Cancer) on an Altera Cyclone IV EP4CE115F29C7 FPGA chip. All models are also implemented on a high performance Xilinx Artix-7 XC7A100TCSG324 FPGA for comparison of the needed hardware resources. Experimental results showing real-time control of the chaotic dynamics are presented.

This paper deals with a safety problem of entropy sources in deterministic random bit generators. An initialization input attack on a set of two pseudo-random generators using analog-digital hardware Trojan is presented. Trojan circuit implementations are discussed following their full classification. Simulation results confirming the effectiveness of the Trojan impact on a repetition of identical seed values are analyzed. Trojan structure is integrated with the deterministic random bit generator functional model recommended by NIST and the task is to impact two seed generators (in two channels), which use the independent Chua circuits as the sources of entropy. The analog Trojan part causes synchronization of the two analog chaotic circuits as explained by the results of LTSpice simulation. The digital Trojan part controls the analog part and modifies the values of optional parameters used in the creation of the seeds. The seed value creation in two cases (with and without Trojan) are simulated by using Xilinx ISIM.

Memristors are widely used in hardware security applications. Research progress in memristor‐based physical unclonable functions (PUFs), random number generators (RNGs), and chaotic circuits is reviewed. To enhance device security, PUFs and RNGs apply randomness of memristors and incorporate 3D crossbars to amplify the number of challenge‐response pairs and provide proof of the destruction of the key, which enables the administrator to firmly control the device information. In addition, the image encryption technique based on the chaotic system is summarized. Furthermore, an assessment of the research advancement in PUFs, RNGs, and chaotic circuits is conducted. This Review examines the characteristics, applications, progress, and challenges of memristors in hardware security and compares the benefits and limitations of different schemes as accelerators for hardware information protection.

Memristors are widely used in hardware security applications. Research progress in memristor‐based physical unclonable functions (PUFs), random number generators (RNGs), and chaotic circuits is reviewed. To enhance device security, PUFs and RNGs apply randomness of memristors and incorporate 3D crossbars to amplify the number of challenge‐response pairs and provide proof of the destruction of the key, which enables the administrator to firmly control the device information. In addition, the image encryption technique based on the chaotic system is summarized. Furthermore, an assessment of the research advancement in PUFs, RNGs, and chaotic circuits is conducted. This Review examines the characteristics, applications, progress, and challenges of memristors in hardware security and compares the benefits and limitations of different schemes as accelerators for hardware information protection. [ABSTRACT FROM AUTHOR]

An exploding demand for processing capabilities related to the emergence of the Internet of Things (IoT), Artificial Intelligence (AI), and big data, has led to the quest for increasingly efficient ways to expeditiously process the rapidly increasing amount of data. These ways include different approaches like improved devices capable of going further in the more Moore path but also new devices and architectures capable of going beyond Moore and getting more than Moore. Among the solutions being proposed, Stochastic Computing has positioned itself as a very reasonable alternative for low-power, low-area, low-speed, and adjustable precision calculations—four key-points beneficial to edge computing. On the other hand, chaotic circuits and systems appear to be an attractive solution for (low-power, green) secure data transmission in the frame of edge computing and IoT in general. Classical implementations of this class of circuits require intensive and precise calculations. This paper discusses the use of the Stochastic Computing (SC) framework for the implementation of nonlinear systems, showing that it can provide results comparable to those of classical integration, with much simpler hardware, paving the way for relevant applications.

The dynamics of nonlinear circuits becomes dependent on the initials setting when memristor is included to design nonlinear circuits, and this memristive circuits can cause distinct transition between periodical and chaotic states by resetting the initial-dependent variables even all the parameters are fixed. A memristive circuit is used to investigate the synchronization stability when the resistor, capacitor, induction coil is applied to connect two identical circuits, respectively. For resistor-based voltage coupling, single channel coupling can realize phase lock even the resistor has to consume more Joule heat with the increase of coupling intensity. In case of capacitor coupling, continuous pump of electric field energy in the coupling capacitor can trigger time-varying electric field and then the phase errors between two circuits are locked. When induction coil is applied to couple two circuits, time-varying magnetic field is triggered to save field energy pumped from the two coupling circuits and then phase errors can also be stabilized. The three kinds of coupling between nonlinear circuits can modulate synchronization via continuous energy exchange and pumping. The coupling resistor just consumes Joule heat while capacitor and induction coil coupling can pump and save field energy and it provide another scheme as field coupling. [ABSTRACT FROM AUTHOR]

The potential application of nonlinear systems and time delay, has a resulted in increasing attention to such systems. In this paper, we designed numerical and circuit models for synchronisation of fractional-order chaotic systems with time delay. Also two fractional order Sprott chaotic systems with time delay is used systems, and, the control circuit is designed for synchronization of the chaotic systems. To provide time delay, all pass filter circuit model has been used. Global stability for the synchronisation is defined according to Lyapunov stability criteria and according to the stability method, the input range is determined to make the system stable. The paper is presented numerical solution of fractional order systems with time delay and designed the circuit model of the system. For different time delay values, the changes in the errors of synchronisation were examined. Finally the results of numerical simulations were compared with the results of circuit analysis to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

Hardware security for an Internet of Things or cyber physical system drives the need for ubiquitous cryptography to different sensing infrastructures in these fields. In particular, generating strong cryptographic keys on such resource-constrained device depends on a lightweight and cryptographically secure random number generator. In this research work, we have introduced a new hardware chaos-based pseudorandom number generator, which is mainly based on the deletion of an Hamilton cycle within the $N$ -cube (or on the vectorial negation), plus one single permutation. We have rigorously proven the chaotic behavior and cryptographically secure property of the whole proposal: the mid-term effects of a slight modification of the seed (proven to be sensitive to the initial conditions) or of the inputted generator cannot be predicted. The proposal has been fully deployed on a FPGA and 65  $\text{nm}$ ASIC, it runs completely in parallel while consuming as low resources as possible, and achieving: (a) 11.5 Gb/s for FPGA and 9.4 Gb/s for ASIC random bit throughput, (b) $3.3\,\mu \text{W}$ (LF) to $7.8 \,\text{mW}$ (UHF) total power consumption with $5\%$ leakage power, measured at $1.32\,\text{V}$ , and (c) able to successfully pass the statistical tests of NIST and TestU01 (BigCrush). [ABSTRACT FROM AUTHOR]

Summary: The paper studies nonlinear dynamics and bifurcations of a class of memristor oscillatory circuits obtained by replacing the nonlinear resistor of a Chua's oscillator with a flux‐controlled memristor. A recently developed technique, named flux‐charge analysis method, has shown that the state space of such circuits can be decomposed in invariant manifolds, where each manifold is characterized by a different dynamics and different attractors. Goal of the paper is to investigate the use of the harmonic balance method in combination with flux‐charge analysis method in order to study the different kinds of bifurcations generated by changing the circuit parameters on a fixed manifold, changing manifold for a fixed parameter set (bifurcations without parameters), or changing simultaneously circuit parameters and manifolds. The main result is that the harmonic balance method is quite simple to apply in this rich bifurcation context and is effective to detect Hopf and to accurately predict period‐doubling bifurcations of all these different kinds. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this study, memristor-based chaotic circuit model is designed and implemented on Field Programmable Gate Array (FPGA). In this chaotic circuit, there are three circuit elements; inductor, capacitor and memristor. The circuit model contains dynamic state equations. In order to obtain chaotic behavior, chaos parameters are given. At first, state equations of chaotic circuit are discretized with Forward Euler method. Theni discrete time chaotic circuit equations are designed on Xilinx System Generator (XSG) in order to simulate chaotic behavior. After simulation process, the design is synthesized and implemented on FPGA through XSG. [ABSTRACT FROM AUTHOR]

The experimental study of a secure chaotic synchronized communication system is presented. The synchronization betweentwo digital chaotic oscillators, serving as a transmitter-receiver scheme, is studied. The oscillators exhibit rich chaotic behaviorand are unidirectionally coupled, forming a master-slave topology. Both the input information signal and the transmittedchaotic signal are digital ones.

The present paper numerically and experimentally demonstrates that an extremely weak diffusive connection can induce a stable periodic orbit in coupled chaotic oscillators, where each individual oscillator has an unstable periodic orbit which dominates its chaotic attractor. The connection-induced stable periodic orbit is quite close to the unstable periodic orbit. The mechanism of this phenomenon is clarified on the basis of bifurcation analysis: When the coupling strength is varied from zero to an extremely small positive value, the unstable periodic orbit embedded within each individual chaotic attractor becomes stable via a period-doubling bifurcation and then disappears via a saddle-node bifurcation. These results are numerically observed in well-known chaotic oscillators, such as Rössler oscillators and logistic maps. Furthermore, an experimental verification of this phenomenon in coupled chaotic electronic circuits is presented. [ABSTRACT FROM AUTHOR]

The brain is characterized by performing many diverse processing tasks ranging from elaborate processes such as pattern recognition, memory or decision making to more simple functionalities such as linear filtering in image processing. Understanding the mechanisms by which the brain is able to produce such a different range of cortical operations remains a fundamental problem in neuroscience. Here we show a study about which processes are related to chaotic and synchronized states based on the study of in-silico implementation of Stochastic Spiking Neural Networks (SSNN). The measurements obtained reveal that chaotic neural ensembles are excellent transmission and convolution systems since mutual information between signals is minimized. At the same time, synchronized cells (that can be understood as ordered states of the brain) can be associated to more complex nonlinear computations. In this sense, we experimentally show that complex and quick pattern recognition processes arise when both synchronized and chaotic states are mixed. These measurements are in accordance with in vivo observations related to the role of neural synchrony in pattern recognition and to the speed of the real biological process. We also suggest that the high-level adaptive mechanisms of the brain that are the Hebbian and non-Hebbian learning rules can be understood as processes devoted to generate the appropriate clustering of both synchronized and chaotic ensembles. The measurements obtained from the hardware implementation of different types of neural systems suggest that the brain processing can be governed by the superposition of these two complementary states with complementary functionalities (nonlinear processing for synchronized states and information convolution and parallelization for chaotic). [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new chaotic system and its corresponding circuit. This system has a special property of having a hidden attractor. Systems with hidden attractors are newly introduced and barely investigated. Conventional methods for parameter estimation in models of these systems have some limitations caused by sensitivity to initial conditions. We use a geometry-based cost function to overcome those limitations by building a statistical model on the distribution of the real system attractor in state space. This cost function is defined by the use of a likelihood score in a Gaussian Mixture Model (GMM) which is fitted to the observed attractor generated by the real system in state space. Using that learned GMM, a similarity score can be defined by the computed likelihood score of the model time series. The results show the adequacy of the proposed cost function. [ABSTRACT FROM AUTHOR]

It has been argued that Lyapunov exponents as a measure of predictability are of limited value because they only provide a global average. Characterizing an attractor by a distribution of times for initial uncertainties to increase by a factor of q has been suggested as a more useful alternative. These have found favor in some applications, despite assumptions of the fictitious perfect model scenario. Here, an electronic circuit, which offers a good test-bed for addressing predictability in the imperfect model scenario, is presented. A novel measure of predictability is presented and implications of model imperfection on characterizing the dynamics of chaotic systems are discussed. It is a case for a multiple model approach. [ABSTRACT FROM AUTHOR]

An implementation of inductorless RC chaotic circuit using FTFN based circuit topology is presented. The design is based on new absolute value nonlinearity circuits. A comparative study is made between two different absolute value nonlinear circuits so as to provide an almost ideal absolute value nonlinearity with no dead region bounded by the two knees due to the i-v characteristics of the diodes, thereby providing an excellent approximation to the absolute value function. [ABSTRACT FROM AUTHOR]

In this paper, the generation of multiscroll chaotic attractors derived from a time-delay differential equation is presented. The proposed system is represented by only one first-order differential equation including time-delayed state variable, and employs hysteresis function as the nonlinear characteristic. The generalization of the introduced system is based on adding multihysteresis nonlinear characteristic which leads to n-scroll chaotic attractors. The circuit implementation of the proposed system and some experimental results referring to two-, three-, four-, and five-scroll chaotic attractors are reported. [ABSTRACT FROM AUTHOR]

The experimental study of in-out intermittency during the incomplete synchronization of two coupled, nonlinear, autonomous, fourth-order, chaotic, circuits is reported. The two circuits are unidirectionally coupled via a linear resistor. The dependence of laminar lengths, on the deviation of the control parameter from its critical value, and the mean laminar length distribution, are studied. [ABSTRACT FROM AUTHOR]

This article introduces a novel three-dimensional continuous autonomous chaotic system with six terms and two quadratic nonlinearities. The new system contains two variational parameters and exhibits Lorenz-like attractors in numerical simulations and experimental measurements. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures, and Lyapunov exponents. The new system examined in Matlab-Simulink® and Orcad-Pspice®. An electronic circuit realization of the proposed system is presented using analog electronic elements such as capacitors, resistors, operational amplifiers and multipliers. The behaviour of the realized system is evaluated with computer simulations. [ABSTRACT FROM AUTHOR]

A new design of Spiking Neural Networks is proposed and fabricated using a 0.35 μm CMOS technology. The architecture is based on the use of both digital and analog circuitry. The digital circuitry is dedicated to the inter-neuron communication while the analog part implements the internal non-linear behavior associated to spiking neurons. The main advantages of the proposed system are the small area of integration with respect to digital solutions, its implementation using a standard CMOS process only and the reliability of the inter-neuron communication. [ABSTRACT FROM AUTHOR]

Abstract: The nonlinear behaviour of an R–L-Varactor circuit, simulated by Multisim 7.0 at a driving frequency that is below the circuit resonance frequency, is reported and evaluated. A new high amplitude oscillation is observed and attributed to the emergence of a large diode junction capacitance. Increasing the driving signal amplitude, the circuit is led to a non-periodic mode of operation, producing trajectories of increasing chaotic content in a four-dimensional phase space. At specific amplitudes a two-dimensional tori was monitored, where trajectories are periodic, like in a two oscillator system with commensurate frequencies. Poincaré cross-sections, FFT spectra and correlation dimension calculations, suggest the quasi-periodicity route to chaos. [Copyright &y& Elsevier]

The experimental study of a secure chaotic synchronized communication system is presented. The synchronization between two digital chaotic oscillators, serving as a transmitter-receiver scheme, is studied. The oscillators exhibit rich chaotic behavior and are unidirectionally coupled, forming a master-slave topology. Both the input information signal and the transmitted chaotic signal are digital ones. [ABSTRACT FROM AUTHOR]

The well-known Matsumoto–Chua–Kobayashi (MCK) circuit is of significance for studying hyperchaos, since it was the first experimental observation of hyperchaos from a real physical system. In this paper, we discuss the existence of hyperchaos in this circuit by virtue of topological horseshoe theory. The two disjoint compact subsets producing a horseshoe found in a specific 3D cross-section, both expand in two directions under the fourth Poincaré return map, this fact means that there exists hyperchaos in the circuit. [ABSTRACT FROM AUTHOR]

The noise-like chaotic signal can be generated with very simple nonlinear circuits, and has broad bandwidth and aperiodic properties. These characteristics have drawn considerable attention in the radar community. In the past, the chaotic signal or its modulated version serves as a transmitting signal, and the traditional correlation-type receiver is used for processing. In this sense, the chaotic signal acts as a radar waveform in the noise signal radar, and hence the performance advantages are not distinct. Here, we present a scheme for processing chaotic radar signals. We find a simple relation between the target parameters (range and velocity) and the system parameters of chaos-generating system. With this relation, the measurement of the target parameters is transformed into estimation of the system parameters from the radar return signals. Equipped with high resolution parameter estimation techniques, the proposed principles provide a way to develop high resolution noise signal radars. [ABSTRACT FROM AUTHOR]

An inductorless realization of nonautonomous (Murali–Lakshmanan–Chua) MLC chaotic circuit is proposed. The main purpose of this study is to improve the performance of nonautonomous MLC chaotic circuit using only CFOAs. CFOA-based topology used in this realization enables to simulate floating inductance. This modification provides to the designer wideband chaotic signals for secure communication systems. In addition to this major improvement, a CFOA-based nonlinear resistor was used in the new realization of nonautonomous MLC chaotic circuit. The usage of CFOA-based inductance simulator and nonlinear resistor in the circuit structure reduces the component count and provides isolated outputs. The performance of the proposed inductorless nonautonomous chaotic circuit is demonstrated with both PSpice simulations and experimental results. [ABSTRACT FROM AUTHOR]

An exploding demand for processing capabilities related to the emergence of the Internet of Things (IoT), Artificial Intelligence (AI), and big data, has led to the quest for increasingly efficient ways to expeditiously process the rapidly increasing amount of data. These ways include different approaches like improved devices capable of going further in the more Moore path but also new devices and architectures capable of going beyond Moore and getting more than Moore. Among the solutions being proposed, Stochastic Computing has positioned itself as a very reasonable alternative for low-power, low-area, low-speed, and adjustable precision calculations—four key-points beneficial to edge computing. On the other hand, chaotic circuits and systems appear to be an attractive solution for (low-power, green) secure data transmission in the frame of edge computing and IoT in general. Classical implementations of this class of circuits require intensive and precise calculations. This paper discusses the use of the Stochastic Computing (SC) framework for the implementation of nonlinear systems, showing that it can provide results comparable to those of classical integration, with much simpler hardware, paving the way for relevant applications. [ABSTRACT FROM AUTHOR]

The spread of epidemics and diseases is known to exhibit chaotic dynamics; a fact confirmed by many developed mathematical models. However, to the best of our knowledge, no attempt to realize any of these chaotic models in analog or digital electronic form has been reported in the literature. In this work, we report on the efficient FPGA implementations of three different virus spreading models and one disease progress model. In particular, the Ebola, Influenza, and COVID-19 virus spreading models in addition to a Cancer disease progress model are first numerically analyzed for parameter sensitivity via bifurcation diagrams. Subsequently and despite the large number of parameters and large number of multiplication (or division) operations, these models are efficiently implemented on FPGA platforms using fixed-point architectures. Detailed FPGA design process, hardware architecture and timing analysis are provided for three of the studied models (Ebola, Influenza, and Cancer) on an Altera Cyclone IV EP4CE115F29C7 FPGA chip. All models are also implemented on a high performance Xilinx Artix-7 XC7A100TCSG324 FPGA for comparison of the needed hardware resources. Experimental results showing real-time control of the chaotic dynamics are presented., (This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.)