On new chaotic and hyperchaotic systems: A literature survey

This paper provides a thorough survey of new chaotic and hyperchaotic systems. An analysis of the dynamic behavior of these complex systems is presented by pointing out their originality and elementary characteristics. Recently, such systems have been increasingly used in various fields such as secure communication, encryption and finance and so on. In practice, each field requires specific performances with peculiar complexity. A particular classification is then proposed in this paper based on the Lyapunov exponent, the equilibriums points and the attractor forms

Design of time delayed chaotic circuit with threshold controller

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.Comment: 21 pages, 12 figures; Submitted to IJB

Dynamics of delay induced composite multi-scroll attractor and its application in encryption

This work was supported in part by NSFC (60804040, 61172070), Key Program of Nature Science Foundation of Shaanxi Province (2016ZDJC-01), Innovative Research Team of Shaanxi Province(2013KCT-04), Fok Ying Tong Education Foundation Young Teacher Foundation(111065), Chao Bai was supported by Excellent Ph.D. research fund (310-252071603) at XAUT.Peer reviewedPostprin

Grid Multiscroll Hyperchaotic Attractors Based on Colpitts Oscillator Mode with Controllable Grid Gradient and Scroll Numbers

AbstractThrough introducing two piecewise-linear triangular wave functions in a three-dimensional spiral chaotic Colpitts oscillator model, a four-dimensional grid multiscroll hyperchaotic system is constructed. Interestingly, by adjusting a build-in parameter in a variable of one triangle wave function, the control of the gradient of the multiscroll grid is achieved. Whereas by deploying the zero points of the two triangular wave functions to extend the saddle-focus equilibrium points with index-2 in phase space the scroll numbers do not only increase along with the number of turning points, but they can also generate arbitrary multiples of products. The basic dynamical behaviors of the proposed four-dimensional multiscroll hyperchaotic system are analyzed. Finally, the hardware experimental circuit is designed and the interrelated circuit implementation is realized. The experimental results are in agreement with both theoretical analyses and numerical simulations, which verify the feasibility of the design methods

A simple method for detecting chaos in nature

Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist's toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

A family of hyperchaotic multi-scroll attractors in Rn

Investigació

A fully CMOS true random number generator based on hidden attractor hyperchaotic system

Low-power devices used in Internet-of-things networks have been short of security due to the high power consumption of random number generators. This paper presents a low-power hyperchaos-based true random number generator, which is highly recommended for secure communications. The proposed system, which is based on a four-dimensional chaotic system with hidden attractors and oscillators, exhibits rich dynamics. Numerical analysis is provided to verify the dynamic characteristics of the proposed system. A fully customized circuit is deployed using 130 nm CMOS technology to enable integration into low-power devices. Four output signals are used to seed a SHIFT-XOR-based chaotic data post-processing to generate random bit output. The chip prototype was simulated and tested at 100 MHz sampling frequency. The hyperchaotic circuit consumes a maximum of 980 μ W in generating chaotic signals while dissipates a static current of 623 μ A. Moreover, the proposed system provides ready-to-use binary random bit sequences which have passed the well-known statistical randomness test suite NIST SP800-22. The proposed novel system design and its circuit implementation provide a best energy efficiency of 4.37 pJ/b at a maximum sampling frequency of 100 MHz