Electronic Simulation and Hardware Implementation of Two Coupled Periodically Forced Duffing and Van der Pol oscillators and its Application to Secure Communication

Confirmation of the existence of complex behavior and synchronization of non-identical chaotic systems as reported in literature attracts much interest in secure communication, but practical implementation is still challenging. In this work, the dynamics of coupled non-identical circuits comprising periodically forced Duffing and Van der Pol oscillators is investigated via electronic simulation using Multism software and hardware implementation on electronic circuits board. After complete synchronization is achieved between the Duffing (Transmitter) and Van der Pol (receiver) circuits through the variation of the coupling resistor of the controller, its application to secure communication is therefore demonstrated experimentally and via multism. The results from the electronic simulation and hardware implementation on bread board using analog components are in good agreement with the numerical results in literature

Quantum internet using code division multiple access

A crucial open problem in large-scale quantum networks is how to efficiently transmit quantum data among many pairs of users via a common data-transmission medium. We propose a solution by developing a quantum code division multiple access (q-CDMA) approach in which quantum information is chaotically encoded to spread its spectral content, and then decoded via chaos synchronization to separate different sender-receiver pairs. In comparison to other existing approaches, such as frequency division multiple access (FDMA), the proposed q-CDMA can greatly increase the information rates per channel used, especially for very noisy quantum channels.Comment: 29 pages, 6 figure

Highly-complex optical signal generation using electro-optical systems with non-linear, non-invertible transmission functions

We present a scheme whereby a static non-linear, non-invertible transmission function performed by the electro-optic Mach-Zehnder modulator produces highly complex optical chaos. The scheme allows the deterministic transformation of low-dimensional band-limited chaotic signals into much higher-dimensional structures with broadband spectra and without using any delay elements or feedback. Standard benchmark tests show that all the considered complexity indices are highly increased due to this transformation in a controlled fashion. This mechanism allows the design of simple optoelectronic delayed oscillators with extremely complex chaotic output.Comment: 4 pages, 5 figures. To appear in Applied Physics Letters (August 2012

Chaos-based communication scheme using proportional and proportional-integral observers

In this paper, we propose a new chaos-based communication scheme using the observers. The novelty lies in the masking procedure that is employed to hide the confidential information using the chaotic oscillator. We use a combination of the addition and inclusion methods to mask the information. The performance of two observers, the proportional observer (P-observer) and the proportional integral observer (PI-observer) is compared that are employed as receivers for the proposed communication scheme. We show that the P-observer is not suitable scheme since it imposes unpractical constraints on the messages to be transmitted. On the other hand, we show that the PI-observer is the better solution because it allows greater flexibility in choosing the gains of the observer and does not impose any unpractical restrictions on the message

Sparse Identification of Nonlinear Duffing Oscillator From Measurement Data

In this paper we aim to apply an adaptation of the recently developed technique of sparse identification of nonlinear dynamical systems on a Duffing experimental setup with cubic feedback of the output. The Duffing oscillator described by nonlinear differential equation which demonstrates chaotic behavior and bifurcations, has received considerable attention in recent years as it arises in many real-world engineering applications. Therefore its identification is of interest for numerous practical problems. To adopt the existing identification method to this application, the optimization process which identifies the most important terms of the model has been modified. In addition, the impact of changing the amount of regularization parameter on the mean square error of the fit has been studied. Selection of the true model is done via balancing complexity and accuracy using Pareto front analysis. This study provides considerable insight into the employment of sparse identification method on the real-world setups and the results show that the developed algorithm is capable of finding the true nonlinear model of the considered application including a nonlinear friction term.Comment: 6 pages, 8 figures, conference pape

Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit

We investigate the dynamics of a driven Van der Pol–Duffing oscillator circuit and show the existence of higher-dimensional chaotic orbits (or hyperchaos), transient chaos, strange-nonchaotic attractors, as well as quasiperiodic orbits born from Hopf bifurcating orbits. By computing all the Lyapunov exponent spectra, scanning a wide range of the driving frequency and driving amplitude parameter space, we explore in two-parameter space the regimes of different dynamical behaviours