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Memristor is a non-linear circuit element in which voltage-current relationship is determined by the previous values of the voltage and current, generally the history of the circuit. The nonlinearity in this component can be considered as a fractional-order form, which yields a fractional memristor (fracmemristor). In this paper, a fractional-order memristor in a chaotic oscillator is applied, while the other electronic elements are of integer order. The fractional-order range is determined in a way that the circuit has chaotic solutions. Also, the statistical and dynamical features of this circuit are analyzed. Tools like Lyapunov exponents and bifurcation diagram show the existence of multistability and antimonotonicity, two less common properties in chaotic circuits. [ABSTRACT FROM AUTHOR]

Chaotic systems and chaos-based applications have been commonly used in the fields of engineering recently. The most essential part of them is the chaotic oscillator that has very critical role in some applications such as chaotic communications and cryptography. In this study, Sundarapandian–Pehlivan chaotic system has been modeled and simulated in three distinct platforms to show the advantages of FPGA-based chaotic oscillator with respect to alternative solutions. In the first stage, the chaotic system has been modeled numerically by the help of fourth order of Runge–Kutta (RK4) method. Additionally, phase portraits of the system have been obtained and Lyapunov exponents have been examined. Secondly, the system has been modeled by using PSpice for the implementation of the chaotic system with analog circuit elements. Then, Pspice simulation results have been compared with the numerical outcome to justify the designed model. Furthermore, the chaotic system has been physically confirmed with real analog circuit elements. Signals obtained from the physical system have been verified with both numerical and PSpice results. It has been also modeled by the help of method of RK4 in a hardware description language (VHDL) and the model further has been synthesized and tested for Xilinx Virtex-6 FPGA chip. Finally, the chaotic oscillator designed has been tested for True Random Number Generators (TRNG) and the maximum operating frequency has been achieved as 293 MHz with a speed of 58.76 Mbit/s. Besides, the random bit sets produced by TRNG have been further verified by FIPS-140-1 and NIST-800-22 statistical standards and it has been proved that the proposed design can be used in embedded cryptologic applications. [ABSTRACT FROM AUTHOR]

Compared to the traditional single scroll and double scroll chaotic systems, multi-scroll chaotic systems present more complex structure and dynamic behavior, possess good application prospect in information security and secure communications. Therefore, theoretical research and circuit implementation of multi-scroll chaotic attractor generation has become a hot spot in the research field of chaos at present domain. In this paper, we briefly overview the recent progress that has been reported in the study of multi-scroll chaotic oscillators based on current-mode devices. Multi-scroll chaotic oscillators are listed according to their electronic implementations. Finally, we list multi-scroll chaotic oscillators based on current-mode devices, and prospect development trends of multi-scroll chaotic oscillators based on current-mode devices in the future. [ABSTRACT FROM AUTHOR]

This paper revisits the design of adaptive impulsive observers (AIOs) for nonlinear systems. The dynamics of observer state of the proposed AIO is modelled by an impulsive differential equation, by which the observer state is updated in an impulsive fashion. The parameter estimation law is modelled by an impulse-free time-varying differential equation associated with the impulse time sequence for determining when the observer state is updated. Unlike the previous work, the convergence analysis of the estimation error system is performed by applying a time-varying Lyapunov function based method, in conjunction with the application of a generalized version of Barbalat’s Lemma. A sufficient condition for the existence of AIOs is also derived. For some special cases, it is shown that the sufficient condition can be formulated in terms of linear matrix inequalities (LMIs), and the observer matrices can be attained by solving a set of LMIs. Furthermore, with an additional persistence-of-excitation-type constraint, it is proved that the sufficient condition can guarantee the convergence of parameter estimation. Two examples of chaotic oscillators are provided to illustrate the design procedure of the proposed AIOs. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose an application of adaptive synchronization of chaos to detect changes in the topology of a mobile robotic network. We assume that the network may evolve in time due to the relative motion of the mobile robots and due to unknown environmental conditions, such as the presence of obstacles in the environment. We consider that each robotic agent is equipped with a chaotic oscillator whose state is propagated to the other robots through wireless communication, with the goal of synchronizing the oscillators. We introduce an adaptive strategy that each agent independently implements to: (i) estimate the net coupling of all the oscillators in its neighborhood and (ii) synchronize the state of the oscillators onto the same time evolution. We show that, by using this strategy, synchronization can be attained and changes in the network topology can be detected. We further consider the possibility of using this information to control the mobile network. We apply our technique to the problem of maintaining a formation between a set of mobile platforms which operate in an inhomogeneous and uncertain environment. We discuss the importance of using chaotic oscillators, and validate our methodology by numerical simulations. [Copyright &y& Elsevier]

Abstract: In this Letter we compare the characteristics of two types of the intermittent behavior (type-I intermittency in the presence of noise and eyelet intermittency taking place in the vicinity of the chaotic phase synchronization boundary) supposed hitherto to be different phenomena. We show that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is confirmed by the consideration of different sample systems, such as quadratic map, Van der Pol oscillator and Rössler system. Consideration of the problem concerning the upper boundary of the intermittent behavior also confirms the validity of the statement on the equivalence of type-I intermittency in the presence of noise and eyelet intermittency observed in the onset of phase synchronization. [Copyright &y& Elsevier]

Abstract: A new method for secure information transmission based on generalized synchronization is proposed. The principal advantage of it is a remarkable stability to noise. To reveal this peculiarity of the proposed method the effectiveness of the detection of the information signal from the transmitted one in the presence of noise in the communication channel is examined both for the proposed scheme and for the schemes of chaotic communication known already. The main ideas of the proposed method are illustrated by the example of coupled Rössler systems used both transmitter and receiver. [Copyright &y& Elsevier]

Abstract: A non-autonomous chaotic circuit which is suitable for high-frequency integrated circuit (IC) realization is presented. Simulation and experimental results verifying the feasibility of the circuit are given. We have numerically verified that the bit streams obtained from the stroboscopic Poincaré map of the system passed the four basic tests of FIPS-140-2 test suite. We also have verified that the binary data obtained from the hardware realization of this continuous-time chaotic oscillator in the same way pass the full NIST random number test suite. Then, in order to increase the output throughput and the statistical quality of the generated bit sequences, we propose a TRNG design which uses a dual oscillator architecture with the proposed continuous-time chaotic oscillator. Finally, we have experimentally verified that the binary data obtained by this oscillator sampling technique pass the tests of full NIST random number test suite without Von Neumann processing for a higher throughput speed while compared with the previous one where the proposed continuous-time chaotic oscillator is used alone. [Copyright &y& Elsevier]

Abstract: Despite its simple mathematical structure, the Sprott E flow displays a chaotic dynamics whose complexity increases with the bifurcation parameter. This complexity shows up in the phase dynamics, which becomes highly incoherent. Such behavior is interpreted as the superposition of the dynamics of several different embedded standard maps. [Copyright &y& Elsevier]

Abstract: This paper presents the result of the investigation of chaotic oscillator synchronization. A new approach to detect the synchronized behaviour of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators. This approach has been applied for the coupled Rössler and Lorenz systems. [Copyright &y& Elsevier]

This work provides a methodology for the control of complex non-linear systems by compensating for the non-linear part using support vector machines (SVM) and subsequently developing simple linear feedback law for control. The method tested for the benchmark Ro¨ssler and Lorenz chaotic oscillators shows excellent performance. [Copyright &y& Elsevier]

Radial basis function networks (RBFNs) are used primarily to solve curve-fitting problems and for non-linear system modeling. Several algorithms are known for the approximation of a non-linear curve from a sparse data set by means of RBFNs. Regularization techniques allow to define constraints on the smoothness of the curve by using the gradient of the function in the training. However, procedures that permit to arbitrarily set the value of the derivatives for the data are rarely found in the literature. In this paper, the orthogonal least squares (OLS) algorithm for the identification of RBFNs is modified to provide the approximation of a non-linear single-input single-output map along with its derivatives, given a set of training data. The interest in the derivatives of non-linear functions concerns many identification and control tasks where the study of system stability and robustness is addressed. The effectiveness of the proposed algorithm is demonstrated with examples in the field of data interpolation and control of non-linear dynamical systems. [Copyright &y& Elsevier]

Abstract: In the above Letter, the authors proposed an interesting approach to design the feedback controller for chaotic systems. However, since the problem how to produce the nonlinear compensation term was not considered, the control scheme present by them is not reasonable and cannot be implemented in general cases. [Copyright &y& Elsevier]