Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, helping also classify and improve the randomness of pseudo-random number sequences generated by iterating chaotic maps.

Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks

Coexisting attractors, circuit implementation and synchronization control of a new chaotic system evolved from the simplest memristor chaotic circuit

We show how to extract messages masked by a chaotic signal of a time-delay system with very high dimension and many positive Lyapunov exponents. Using a special embedding coordinate, the infinite dimensional phase space of the time-delay system is projected to a special three-dimensional space, which enables us to identify the time-delay of the system from the transmitted signal, and reconstruct the chaotic dynamics to unmask the hidden message successfully. The message extraction procedure is illustrated by simulations with Mackey-Glass time-delay system for two type of masking schemes and different kinds of messages.

Extracting Messages Masked by Chaotic Signals of Time-delay Systems

By replacing the resistor in a Twin-T network with a generalized flux-controlled memristor, this paper proposes a simple fourth-order memristive Twin-T oscillator. Rich dynamical behaviors can be o...

Various Attractors, Coexisting Attractors and Antimonotonicity in a Simple Fourth-Order Memristive Twin-T Oscillator

In this paper, the hyperchaos analysis, optimal control, and synchronization of a nonautonomous cardiac conduction system are investigated. We mainly analyze, control, and synchronize the associated hyperchaotic behaviors using several approaches. More specifically, the related nonlinear mathematical model is firstly introduced in the forms of both integer- and fractional-order differential equations. Then the related hyperchaotic attractors and phase portraits are analyzed. Next, effectual optimal control approaches are applied to the integer- and fractional-order cases in order to overcome the obnoxious hyperchaotic performance. In addition, two identical hyperchaotic oscillators are synchronized via an adaptive control scheme and an active controller for the integer- and fractional-order mathematical models, respectively. Simulation results confirm that the new nonlinear fractional model shows a more flexible behavior than its classical counterpart due to its memory effects. Numerical results are also justified theoretically, and computational experiments illustrate the efficacy of the proposed control and synchronization strategies.

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Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system

The constraints of a wireless physical media, such as multi-path propagation and complex ambient noises, prevent information from being communicated at low bit error rate. Surprisingly, it has only recently been shown that, from a theoretical perspective, chaotic signals are optimal for communication. It maximises the receiver signal-to-noise performance, consequently minimizing the bit error rate. This work demonstrates numerically and experimentally that chaotic systems can in fact be used to create a reliable and efficient wireless communication system. Toward this goal, we propose an impulsive control method to generate chaotic wave signals that encode arbitrary binary information signals and an integration logic together with the match filter capable of decreasing the noise effect over a wireless channel. The experimental validation is conducted by inputting the signals generated by an electronic transmitting circuit to an electronic circuit that emulates a wireless channel, where the signals travel along three different paths. The output signal is decoded by an electronic receiver, after passing through a match filter.

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Experimental validation of wireless communication with chaos

A novel chaotic spread spectrum acoustic communication method is proposed in this paper. A chaotic signal, generated by a hybrid dynamical system, is used as spread spectrum sequence and the corresponding chaotic matched filter is used to decrease the effect of multiple propagation and noises. The proposed method does not need the complicated channel modulation-demodulation and equalization technologies, which are necessary for conventional acoustic communication. Simulation results show the proposed method has lower BER as compared to some existing methods.

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A chaotic spread spectrum system for underwater acoustic communication

In this work, an enhanced differential chaos shift keying (DCSK), based on a first order hybrid chaotic system, is being proposed for a high reliability underwater acoustic communication system. It can be integrated into systems that use standard existing transducers. We show that a coherent operation between the received signal and the time reversal of the basis function in a first order hybrid chaotic system maximizes the signal to noise ratio at the receiver. Concurrently, DCSK configuration is used to resist the distortion caused by the complex underwater acoustic channel. Our simulation results show that the proposed method has lower bit error rate (BER). In addition, it shows higher communication reliability over underwater acoustic channel as compared to the conventional DCSK using logistic map and its variant forms such as Correlation Delay Shift Keying (CDSK), Phase-Separate DCSK (PS-DCSK), High Efficiency DCSK (HE-DCSK), and Reference Modulated DCSK (RM-DCSK).

Chaos-Based Underwater Communication With Arbitrary Transducers and Bandwidth

An experimental secure communication method based on the Chen system with time-delay is being proposed in this paper. The Chen system with time-delay is an infinite-dimensional system having more than one positive Lyapunov exponent. The message to be transmitted is encrypted using an hyperchaotic signal generated by the Chen system with time-delay and multishift cipher function. This encryption makes difficult for an eavesdropper to reconstruct the attractor by using time-delay embedding techniques, return map reconstruction, or spectral analysis, consequently, improving the security. Simulations and experiments on TI TMS320C6713 Digital Signal Processor (DSP) show improved resilience against attack and the feasibility of the proposed scheme.

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Secure Communication Based on Hyperchaotic Chen System with Time-Delay

An M-ary Differential Chaos Shift Keying modulation using Chaotic Shape-forming Filter (CSF-M-DCSK) is proposed here to transmit two sub-streams with different system performances. The chaotic shape-forming filter is used to generate the chaotic carrier which is modulated according to the DCSK concept. The modulated chaotic signal is demodulated by a coherent matched filter receiver and the maximum likelihood decision rule is used to get the best noise performance. Compared to DCSK and its enhanced versions, the new modulation scheme offers not only better noise and multipath performances but also a higher data rate. The hardware implementation of the proposed method is as simple as that of a conventional communication system. Analytical expressions have been derived for the CSF-M-DCSK Bit Error Rate (BER) and its performance has been evaluated in AWGN and multipath channels by simulations. The new CSF-M-DCSK system has been implemented and successfully tested on a Wireless open-Access Research Platform (WARP). Results of simulations and measurements performed in real application scenarios have proven the feasibility and superiority of CSF-M-DCSK over its competitors.

Chao Bai

Papers

Experimental validation of wireless communication with chaos

A chaotic spread spectrum system for underwater acoustic communication

Chaos-Based Underwater Communication With Arbitrary Transducers and Bandwidth

Secure Communication Based on Hyperchaotic Chen System with Time-Delay

Double-Sub-Stream M-ary Differential Chaos Shift Keying Wireless Communication System Using Chaotic Shape-Forming Filter