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Time-delayed dynamical systems generally feature smooth nonlinear transfer functions in the feedback loop, such as polynomial or sinusoidal functions. As a consequence, the complexity of their dynamical behavior mainly originates from the time-delay. In this paper, we explore the opposite case where the nonlinear transfer function is complex ( $cos^{2}(sinh)$ ), and therefore, non-smooth. We perform a bifurcation analysis of the system, and evidence that this novel type of time-delayed system can display a chaotic behavior characterized by positive maximum Lyapunov exponent and quasi-maximal entropy. The high entropy behavior of the system combined with post-processing are used to generate random numbers for small values of the feedback gain with an overall bit rate up to 1.478 Gb/s. Our theoretical results are in excellent agreement with experimental measurements, performed with an optoelectronic oscillator involving a complex transfer function designed ad hoc .

This document presents the design of a prototype of a low-cost personal weather station suitable for farmers in rural areas who are or may not be engaged in rudimentary agriculture. This prototype measure several weather data: temperature, relative humidity, wind speed, wind direction, rainfall. For further data analysis, these are transmitted for recording to a remote server via wireless communication. The server offers data extraction possibilities in multiple file formats. A prototyping of the personal weather station is designed and commissioned. An extract of the results over two days is presented in the results section of this document

This paper reports a new kind of mathematical model for language competition dynamics using compartmental epidemiological modeling approach. The model describes the competition between two languages, say the predominant one called language 1, and the less spoken language 2, both in the same community. We distinguish three groups of population building the concerned community: one majority speaking language 1, one minority speaking language 2 and a last minority speaking neither language 1 nor language 2. The study of the proposed model includes an analysis of the evolution of the number of speakers over time. This model predicts that language 2 can inevitably disappear if the threshold parameter $${\mathcal {R}}_0$$ is less than one. We show that our model is well-posed mathematically and linguistically. We also show that the model has basically two linguistic equilibrium points. A monolingual equilibrium point that corresponds to the case where only one language is spoken: some individuals speak only the language 1 and some others do speak neither language 1, nor language 2. A bilingual equilibrium point which corresponds to the case where all the languages are spoken: some individuals speak both languages 1 and 2, some others speak only language 1, while a third group does speak only language 2, and the last group speaks none of the two languages. In this bilingual equilibrium point, both languages coexist. Depending on the threshold parameter, we demonstrate the stability of these equilibria. The model presents on one hand, a direct bifurcation phenomenon, in which we have a stable equilibrium point without bilingual speakers when the associated basic reproduction number is less than one. On the other hand, it presents a stable bilingual equilibrium point when the number of associated basic reproductions is greater than one. The analysis of the overall sensitivity of the model is performed and the impact of the system parameters on the basic reproduction number was performed using sensitivity analysis to determine the impact of each parameter of the system on bilingualism. The numerical simulations carried out are in agreement with the presented theory

A simple 5D hyperchaotic system recently introduced in the literature is modified by using a charge-controlled memristor model and striking behaviors are uncovered. The resulting system is a 6D hyperchaotic system, which generates hidden attractors with the unusual feature of having plan and line equilibrium under different parameter conditions. Its dynamical behaviors are characterized through bifurcation diagrams, Lyapunov exponents, phase portraits, Poincare sections and time series. Rich nonlinear dynamics such as limit cycles, quasi-periodicity, chaos, hyperchaos, bursting and hidden extreme multistability are found for appropriate sets of parameter values. The high complexity of the system is confirmed by its Kaplan–yorke dimension (greater than five). Additionally, an electronic circuit is designed to implement the novel system and PSpice simulation results are in good accordance with the numerical investigations. To the best of our knowledge, this system is the first with higher order presenting all those phenomena.

This paper presents a 6D autonomous system, obtained by introducing a flux-controlled memristor model into an existing 5D hyperchaotic autonomous system. The dynamics of the novel system are investigated in terms of equilibrium points, bifurcation diagrams, Lyapunov exponent spectra, phase portraits, time series and attraction basins. Moreover, its circuit implementation is also proposed. The system is hyperchaotic under a line or a plan of equilibria. Other attractive dynamics observed are: hidden extreme multistability, transient chaos, bursting and offset boosting phenomenon. Interestingly, for a particular set of parameters, an unusual metastability showing transition from chaotic to periodic bursting dynamics is found. Dynamical systems capable of producing the above complexity are not common in the literature; thus, this novel memristive 6D hyperchaotic autonomous system deserves particular attention. PSpice based simulations are in good agreement with numerical computations. To the best of our knowledge, this system is the first with higher order presenting all those phenomena.

Made available in DSpace on 2022-04-28T17:21:57Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-06-08 ICTP-SAIFR Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) The phenomenon of the chimera state symbolizes the coexistence of coherent and incoherent sections of a given population. This phenomenon identified in several physical and biological systems presents several variants, including the multichimera states and the traveling chimera state. Here, we numerically study the influence of a weak external electric field on the dynamics of a network of Hindmarsh-Rose (HR) neurons coupled locally by an electrical interaction and nonlocally by a chemical one. We first focus on the phenomena of traveling chimera states and multicluster oscillating breathers that appear in the electric field's absence. Then in the field's presence, we highlight the presence of a chimera state, a multichimera state, an alternating chimera state, and a multicluster traveling chimera. Univ Dschang, Fac Sci, Dept Phys, Res Unit Condensed Matter Elect & Signal Proc, POB 67, Dschang, Cameroon Sao Paulo State Univ UNESP, Inst Fis Teor, Rua Doutor Bento Teobaldo Ferraz 271,Bloco 2, BR-01140070 Barra Funda, SP, Brazil Univ Ulm, Inst Surface Chem & Catalysis, Albert Einstein Allee 47, D-89081 Ulm, Germany Gomez & Gomez Ltda ME, Epistem, Cietec, Ave Prof Lineu Prestes 2242,Sala 244, BR-05508000 Sao Paulo, Brazil Sao Paulo State Univ UNESP, Inst Fis Teor, Rua Doutor Bento Teobaldo Ferraz 271,Bloco 2, BR-01140070 Barra Funda, SP, Brazil FAPESP: 2016/01343-7 CAPES: 001

This paper presents a novel fourth-order autonomous flux controlled memristive Wien-bridge system. Standard nonlinear diagnostic tools such as bifurcation diagram, graphs of largest Lyapunov exponent, Lyapunov stability diagram, phase space trajectory and isospike diagram are used to characterize dynamics of the system. Results show that the system presents hidden attractors with infinite equilibrium points known as line equilibrium for a suitable set of its parameters. The system also exhibits striking phenomenon of extreme multistability. Through isospike and Lyapunov stability diagram, spiral bifurcation leading to a center hub point is observed in a Wien-bridge circuit for the first time and the Field Programmable Gate Array -based implementation is performed to confirm its feasibility.

This paper is investigating the hyperchaotic dynamics of a novel hyperchaotic oscillator (made of only three electronics components namely a transformer, a capacitor and a junction field effect transistor (JFET)) obtained by modifying the simple chaotic circuit proposed by Tchitnga et al. (doi:10.1016/j.chaos.2011.12.017) and published within this journal. The various laboratory tests on the novel three components oscillator help to confirm that it operates at high frequencies. Henceforth, justified the choice of Giacolleto model of JFET. Hyperchaos is analysed using well known nonlinear dynamic tools including bifurcation diagrams, Lyapunov exponent spectrum, phase portraits and Poincare sections. Likewise, the high frequency is confirmed through the frequency spectrum simulated with PSpice. The systems also present the striking phenomena of hysteretic dynamics (bistability) and transient chaos as well as bursting oscillations over a wide range of its control parameter region. The measurements from experimental investigations are in accordance with the obtained numerical results.

We report the modeling for analysis of electrical clippers with side to side oscillating blade. The mathematical expressions for the study of its electromechanical dynamics are derived from the application of electromagnetics as well as mechanics laws. Numerical and analytical investigations reveal that, for well chosen range of its control parameters the efficiency of such clippers can be significantly improved, while the electrical power consumption is optimized. Chaotic behavior is investigated numerically using bifurcations diagrams. Experimental results match up well the theoretical predictions.

The relay coupling of three fractional-order two-stage oscillators in the presence of time delay has been explored theoretically, numerically and analogically. The global stabilization of the system in a finite time is proven through Holder and Gronwall inequalities, as well as through inequality scaling skills. The Synchronization of the system is characterized in terms of its parameters (coupling strength and time delay) by using time series, two parameters phase diagrams and two parameters transverse Lyapunov exponent diagrams. It is found that for smaller delay values, the network exhibits global phase synchronization whereas for higher delay values, phase synchronization just occurs between the two indirectly connected units (cluster phase synchronization). Striking phenomena such as amplitudes’ death and chaotic beats oscillations are also observed from this relay coupling of three fractional-order two-stage oscillators. Furthermore, PSpice simulation results of the analog electronic circuit are in perfect accordance with both theoretical and numerical results.

Inductive devices with ferromagnetic core are widely used in many electronic circuits to store magnetic energy. They should be treated as nonlinear devices, and the nonlinearity of their characteristics arises from the dependence of inductance on current. Such inductors display saturation and hysteresis behaviors. In the present paper, we report a new mathematical model based on the experimental data of hysteresis for ferromagnetic core inductors. We used the model to determine analytically the expression of current in a RLC series circuit forced by an alternating source. Multi periodic and high amplitude chaotic signals are observed and good agreement is found between theoretical and experimental results.

We study the emergence of the traveling chimera state in a two-dimensional network of Hindmarsh-Rose burst neurons with the mutual presence of local and non-local couplings. We show that in the unique presence of the non-local chemical coupling modeled by a nonlinear function, the traveling chimera phenomenon occurs with a displacement in both directions of the plane of the grid. The introduction of local electrical coupling shows that the mutual influence of the two types of coupling can, for certain values, generate traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera, ie the presence in the network under study, of patterns of coherent elements interspersed by other incoherent elements in movement and alternately changing their position over time. The confirmation of the states of coherence is done by introducing the parameter of instantaneous local order parameter in two dimensions. We extend our analysis through mathematical tools such as the Hamilton energy function to determine the direction of propagation of patterns in two dimensions., 8 pages, 8 figures, Accepted for publication in Physics Letters A (2021)

We study bifurcations and chaotic behavior of a periodically forced lever that is magnetically controlled. The system is extremely simple and low cost and can be assembled in a very short time. Both the theoretical simulations and the experimental measurements exhibit regions of periodic and chaotic behaviors, depending on the system parameters. Amplitude jumps, hysteresis and bistable states are also observed. The wide possibilities of varying the system parameters make the experiments suitable for demonstrations. Good agreements are found between our theoretical results and experimental ones.

The paper is devoted to theoretical and experimental investigations of an electromechanical system consisting of DC motor, a physical pendulum with the repulsive magnets. The work consists of modeling, simulation and experimental measurements to validate the analytical predictions and the numerical simulation of the earlier introduced mathematical model. The parameters of the model are estimated using the experimental data. The analyzed system shows several types of non-linear effects, including hysteresis, jump phenomena, chaos and periodic dynamics. Good agreement between real and simulated behavior of the system is obtained.

A simple driven bipolar junction transistor (BJT) based two-component circuit is presented, to be used as didactic tool by Lecturers, seeking to introduce some elements of complex dynamics to undergraduate and graduate students, using familiar electronic components to avoid the traditional black-box consideration of active elements. Although the effect of the base-emitter (BE) junction is practically suppressed in the model, chaotic phenomena are detected in the circuit at high frequencies (HF), due to both the reactant behavior of the second component, a coil, and to the birth of parasitic capacitances as well as to the effect of the weak nonlinearity from the base-collector (BC) junction of the BJT, which is otherwise always neglected to the favor of the predominant but now suppressed base-emitter one. The behavior of the circuit is analyzed in terms of stability, phase space, time series and bifurcation diagrams, Lyapunov exponents, as well as frequency spectra and Poincaré map section. We find that a limit cycle attractor widens to chaotic attractors through the splitting and the inverse splitting of periods known as antimonotonicity. Coexisting bifurcations confirm the existence of multi-stability behaviors, marked by the simultaneous apparition of different attractors (periodic and chaotic ones) for the same values of system parameters and different initial conditions. This contribution provides an enriching complement in the dynamics of simple chaotic circuits functioning at high frequencies. Experimental lab results are completed with PSpice simulations and theoretical ones., Education; Electrical engineering; Nonlinear physics; Antimonotonicity; Bipolar junction transistor; Chaos; Didactic model; High frequency; Multistability; Parasitic capacitance

Made available in DSpace on 2019-10-06T16:27:35Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-04-18 We design and report an electrical circuit using a Josephson junction under periodic forcing that reveals extreme multistability. Its overall state equations surprisingly recall those of a well-known model of Josephson junction initially introduced in our circuit. The final circuit is characterized by the presence of two new and different current sources in parallel with the nonlinear internal current source sin[φ(t)] of the Josephson junction single electronic component. Furthermore, the model presents an interesting extreme multistability which is justified by a very large number of different attractors (chaotic or not) when slightly changing the initial conditions. São Paulo State University - UNESP Instituto de Física Teórica, Rua Doutor Bento Teobaldo Ferraz 271 Research Unit Condensed Matter Electronics and Signal Processing Université de Dschang, P.O. Box 67 Center for Interdisciplinary Research on Complex Systems University of Sao Paulo, Avenida Arlindo Bettio 1000 Nuclear Technology Section Institute of Geological and Mining Research, P.O. Box 4110 Instituto de Física Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48 São Paulo State University - UNESP Instituto de Física Teórica, Rua Doutor Bento Teobaldo Ferraz 271

This paper addresses the problem of generalized finite-time function projective synchronization (GFFPS) of fractional-order chaotic systems. A modified fractional nonsingular terminal sliding mode surface and an appropriate robust fractional sliding mode control law are proposed, taking into account the effects of model uncertainties and of the external disturbances. An appropriate Lyapunov functional candidate is used to prove the finite-time existence of the sliding motion. Compared with the existing nonsingular sliding mode surface, our sliding mode surface permits to reduce the settling time of synchronization. Finally, some numerical simulations taking into consideration the Gaussian white noise produced by the electrical line are presented to demonstrate the effectiveness and applicability of the proposed technique.

A novel model of general purpose operational amplifiers is made to approximate, at best, the equivalent circuit for real model at high-frequency. With this new model, it appears that certain oscillators, usually studied under ideal considerations or using many existing real models of operational amplifiers, have hidden subtle and attractive chaotic dynamics that have previously been unknown. These can now be revealed. With the new considerations, a “two-component” circuit, consisting simply of a capacitor in parallel with a nonmodified (and usually presented as a linear, negative) resistance, tends to exhibit chaotic signals. P-Spice and laboratory experimental results are in good agreement with the theoretical predictions.

Made available in DSpace on 2020-12-12T02:15:46Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-06-15 In the literature, existing Josephson junction based oscillators are mostly driven by external sources. Knowing the different limits of the external driven systems, we propose in this work a new autonomous one that exhibits the unusual and striking multiple phenomena among which coexist the multiple hidden attractors in self-reproducing process under the effect of initial conditions. The eight-term autonomous chaotic system has a single nonlinearity of sinusoidal type acting on only one of the state variables. A priori, the simplicity of the system does not predict the richness of its dynamics. We also find that a limit cycle attractor widens to a parameter controlling coexisting multiple-scroll attractors through the splitting and the inverse splitting of periods. Multiple types of bifurcations are found including period-doubling and period-splitting (antimonotonicity) sequences to chaos, crisis and Hopf type bifurcation. To the best of our knowledge, some of these interesting phenomena have not yet been reported in similar class of autonomous Josephson junction based circuits. Moreover, analytical investigations based on the Hopf theory analysis lead to the expressions that determine the direction of appearance of the Hopf bifurcation, confirming the existence and determining the stability of bifurcating periodic solutions. To observe this latter bifurcation and to illustrate the theoretical analysis, numerical simulations are performed. Chaos can be easily controlled by the frequency of the linear oscillator, the superconducting junction current, as well as the gain of the amplifier or circuit component values. The circuit and Field Programmable Gate Arrays (FPGA)-based implementation of the system are presented as well. Research Group on Experimental and Applied Physics for Sustainable Development Faculty of Science Department of Physics University of Dschang, P. O. Box 412 Laboratory of Condensed Matter Electronics and Signal Processing Department of Physics University of Dschang, P. O. Box 067 Department of Physics Higher Teacher Training College University of Bamenda, P. O. Box 39 Institute of Surface Chemistry and Catalysis University of Ulm, Albert-Einstein-Allee 47 Instituto de Fisica Teorica - UNESP Universidade Estadual Paulista Rua Dr. Bento Teobaldo Ferraz, 271, Bloco II, Barra Funda Laboratoire de Mécanique et de Modélisation des Systèmes L2MS Department of Mathematics and Computer Science Faculty of Science University of Dschang, P. O. Box 67 Instituto de Fisica Teorica - UNESP Universidade Estadual Paulista Rua Dr. Bento Teobaldo Ferraz, 271, Bloco II, Barra Funda

This work deals with the electrical characterization of a piezoelectric plate and its use to generate self-sustained electrical and mechanical oscillations. An experimental frequency-impedance curve of the piezoelectric plate is obtained leading to the electric equivalent of the piezoelectric plate constituted of a capacitive branch in parallel with many RLC resonant branches. The values of the electric components for each branch are determined using the resonant and anti-resonant frequencies. It is demonstrated theoretically that these branches can be understood in terms of vibration modes of the plate; each of which has its own resonant frequency. It is then demonstrated theoretically and experimentally that putting the piezoelectric plate in series with a resistor presenting a nonlinear I − V characteristics having a negative slope, autonomous oscillations of the Van der Pol type can be observed. A theoretical development has led to the appearance of self-sustained periodic and mixed modes mechanical oscillations of the plate deflection.

In this paper, a fractional-order version of a chaotic circuit made simply of two non-idealized components operating at high frequency is presented. The fractional-order version of the Hopf bifurcation is found when the bias voltage source and the fractional-order of the system increase. Using Adams–Bashforth–Moulton predictor–corrector scheme, dynamic behaviors are displayed in two complementary types of stability diagrams, namely the two-parameter Lyapunov exponents and the isospike diagrams. The latest being a more fruitful type of stability diagrams based on counting the number of spikes contained in one period of the periodic oscillations. These two complementary types of stability diagrams are reported for the first time in the fractional-order dynamical systems. Furthermore, a new fractional-order adaptive sliding mode controller using a reduced number of control signals was built for the stabilization of a fractional-order complex dynamical network. Two examples are shown on a fractional-order complex dynamical network where the nodes are made of fractional-order two-component circuits. Firstly, we consider an ideal channel, and secondly, a non ideal one. In each case, increasing of the coupling strength leads to the phase transition in the fractional-order complex network.

The queue of patients for consultation and appointments that we observe in our health centers is growing in size from day to day given the exponential growth of the human population. Medical systems based on telemonitoring have been developed to remotely monitor the health status of patients. In this work, we constructed a medical prototype for remote monitoring of the mechanical activity of the heart and for geolacalization of the patient based on Message Queue Telemetry Transport (MQTT). The prototype will be used by individuals or by health centers without a doctor. The geolacalization will enable us to locate the injured individual. The physiological data and GPS coordinates are collected using a portable kit and are transmitted directly to an MQTT cloud using a Wi-Fi hotspot. A web server hosted in the kit allows the user to enter the service set identifier (SSID) of the access point through a smartphone. MQTT cloud will take care of the storage, geolacalization and transmission of the signal from the mechanical activity of the heart to the doctors. Almost all smart terminals with a web browser can easily access data (smartphone, tablet, computer). Tests carried out on individuals reveal that the proposed prototype is reliable in sampling, real-time transmission and geolacalization in street map and imagery, which can help in diagnosis and rapid intervention.

Made available in DSpace on 2018-12-11T17:15:47Z (GMT). No. of bitstreams: 0 Previous issue date: 2017-10-18 We report a simple model of two drive-response-type coupled chaotic oscillators, where the response system copies the nonlinearity of the driver system. It leads to a coherent motion of the trajectories of the coupled systems that establishes a constant separating distance in time between the driver and the response attractors, and their distance depends upon the initial state. The coupled system responds to external obstacles, modeled by short-duration pulses acting either on the driver or the response system, by a coherent shifting of the distance, and it is able to readjust their distance as and when necessary via mutual exchange of feedback information. We confirm these behaviors with examples of a jerk system, the paradigmatic Rössler system, a tunnel diode system and a Josephson junction-based jerk system, analytically, to an extent, and mostly numerically. São Paulo State University (UNESP) Instituto de Física Teórica, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II Laboratory of Electronics and Signal Processing Faculty of Science Department of Physics University of Dschang, P.O. Box 67 Dumkal Institute of Engineering and Technology Department of Instrumentation and Electronics Engineering Jadavpur University Institute of Surface Chemistry and Catalysis University of Ulm, Albert-Einstein-Allee 47 Department of Physics Bharathidasan University Department of Mathematics Jadavpur University Centre for Complex System Research Kolkata São Paulo State University (UNESP) Instituto de Física Teórica, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II

The problem of finite-time synchronization of fractional-order simplest two-component chaotic oscillators operating at high frequency and application to digital cryptography is addressed. After the investigation of numerical chaotic behavior in the system, an adaptive feedback controller is designed to achieve the finite-time synchronization of two oscillators, based on the Lyapunov function. This controller could find application in many other fractional-order chaotic circuits. Applying synchronized fractional-order systems in digital cryptography, a well secured key system is obtained. Numerical simulations are given to illustrate and verify the analytic results.

In the framework of a project on simple circuits with unexpected high degrees of freedom, we report an autonomous microwave oscillator made of a CLC linear resonator of Colpitts type and a single general purpose operational amplifier (Op-Amp). The resonator is in a parallel coupling with the Op-Amp to build the necessary feedback loop of the oscillator. Unlike the general topology of Op-Amp-based oscillators found in the literature including almost always the presence of a negative resistance to justify the nonlinear oscillatory behavior of such circuits, our zero resistor circuit exhibits chaotic and hyperchaotic signals in GHz frequency domain, as well as many other features of complex dynamic systems, including bistability. This simplest form of Colpitts oscillator is adequate to be used as didactic model for the study of complex systems at undergraduate level. Analog and experimental results are proposed., Electrical engineering; Nonlinear physics; Operational Amplifier; High Frequency; Parasitic Capacitances; Hyperchaos; Bistability.

This article is investigating from one of best control technique known as periodically intermittent discrete observation control (PIDOC), the problem of global synchronization based on a relay configuration of three novel hyperchaotic oscillators of three-components (NHO) operating at high frequency. Contrary to traditional periodically intermittent control based on continuous-time state observations, PIDOC used here, chooses discrete-time state observations in work time during a control period. Our analysis has been limited to a range of parameters for which the NHO-type oscillator exhibits bursting oscillations. The global conditions of stability for non-adaptive and adaptive cases have been proven analytically. To the best of our knowledge and in the literature of the relay coupling system, no work has been carried out concerning the study of the stability of adaptive synchronization case. The Synchronization of the system is analysed in terms of its control gain by using time series. The numerical results show that there is global synchronization between the three relay coupled NHO-type oscillators for both non-adaptive and adaptive synchronizations. Moreover, PSpice based simulations of the analog electronic circuit for the non-adaptive case are in good accordance with both theoretical and numerical results.

The dynamics and robust finite-time hybrid projective synchronization of a fractional-order four-dimensional nonlinear system based on a two-stage Colpitts oscillator is investigated. The study of the fractional order stability of the equilibrium states of the system is carried out. The bifurcation diagram confirms the occurrence of Hopf bifurcation in the proposed system when the fractional-order passes a sequence of critical values; the Lyapunov exponent shows the different chaotic sequences of the system. Further, a fractional nonsingular terminal sliding surface and an appropriate robust fractional sliding mode control law are proposed for the finite-time hybrid projective synchronization of a fractional-order chaotic two-stage Colpitts oscillator by taking into account the effects of model uncertainties and the external disturbances. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. Finally, some numerical simulations are presented to demonstrate the effectiveness and applicability of the proposed technique.

Firstly, the synchronization problem of the simplest two-component Hartley chaotic systems is considered. A simple and effective controller is used to achieve synchronization between the drive and response systems. The proposed controller is built around a linear and a nonlinear parts with each contributing to the achievement of the synchronization process. The stability of the drive–response systems framework is proved through the Lyapunov stability theory. Secondly, the impact of channel on the signal coming from the drive system to synchronize the response system is taken into consideration. In this second part, the conditions to obtain synchronization between both master and slave systems are investigated. For the purpose of illustration, PSpice simulations are given as complement of the numerical analysis.

This paper shows an experimental evidence of chaos in one of the simplest imaginable autonomous implicit Hartley’s oscillator made simply of a junction field effect transistor (JFET) and a tapped coil. The experimental setup is implemented. The variations of amplitude of the oscillations through the control element are obtained showing the domain of existence of chaos. Phase portraits of the PSpice simulation, of the numerical integration and of the experiment are displayed, confirming a good agreement between theory and praxis.

This paper exposes circuit design of linear congruential generator (LCG) and implementation in FPGA based on block reduction technique. The circuit is derived from LCG algorithm proposed by Lehmer. Block reduction technique has been used to simplify the circuit. Several net connections among the blocks of the circuit are ignored or disconnected and the multiplier is replaced by a shifter. Simulations of both behavior and timing have been done and the results confirm its algorithm. The Cyclone II EP2C8Q208C8N and Cyclone IV E EP4CE115F29C7N of Altera have been chosen to extract comparison data of speed and occupied area. Further comparison of shift technique and the wordlengths reduction technique has been made. In general, the proposed design is far simpler than the previous published LCG circuit.