National Institute of Standards and Technology における超伝導研究及び生活

This letter reports the finding of a new chaotic attractor in a simple three-dimensional autonomous system, which connects the Lorenz attractor and Chen's attractor and represents the transition from one to the other.

http://lsc.amss.ac.cn/~ljh/02LC.pdf?origin=publication_detail

A new chaotic attractor coined

A novel colour image encryption algorithm based on chaos

Over the last two decades, theoretical design and circuit implementation of various chaos generators have been a focal subject of increasing interest due to their promising applications in various ...

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Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications

When chaotic systems are realized with finite precisions in digital computers, their dynamical properties are often found to be entirely different from the original versions in the continuous setting. In the literature, there does not seem to be much work on quantitative analysis of such degradation of digitized chaos and how to reduce its negative influence on chaos-based digital systems. Focusing on 1D piecewise linear chaotic maps (PWLCM), this paper reports some findings on a new series of dynamical indicators, which can quantitatively reflect the degradation effects on a digital PWLCM realized with a fixed-point finite precision. On top of that, the paper introduces a new method for studying digital chaos from an algorithmic point of view. In addition, the theoretical results obtained in this paper should be very helpful for the consideration of reducing negative influence of dynamical degradation in real design of various digital chaotic systems. As typical examples, the proposed dynamical indicators are applied to the performance comparison of different remedies for improving dynamical degradation, cryptanalysis of digital chaotic ciphers based on 1D PWLCM, and design of chaotic pseudo-random number generators with desired characteristics.

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On the dynamical degradation of digital piecewise linear chaotic maps

Memristors can be employed to mimic biological neural synapses or to describe electromagnetic induction effects. To exhibit the threshold effect of electromagnetic induction, this paper presents a threshold flux-controlled memristor and examines its frequency-dependent pinched hysteresis loops. Using an electromagnetic induction current generated by the threshold memristor to replace the external current in 2-D Hindmarsh–Rose (HR) neuron model, a 3-D memristive HR (mHR) neuron model with global hidden oscillations is established and the corresponding numerical simulations are performed. It is found that due to no equilibrium point, the obtained mHR neuron model always operates in hidden bursting firing patterns, including coexisting hidden bursting firing patterns with bistability also. In addition, the model exhibits complex dynamics of the actual neuron electrical activities, which acts like the 3-D HR neuron model, indicating its feasibility. In particular, by constructing the fold and Hopf bifurcation sets of the fast-scale subsystem, the bifurcation mechanisms of hidden bursting firings are expounded. Finally, circuit experiments on hardware breadboards are deployed and the captured results well match with the numerical results, validating the physical mechanism of biological neuron and the reliability of electronic neuron.

Hidden Bursting Firings and Bifurcation Mechanisms in Memristive Neuron Model With Threshold Electromagnetic Induction

This Letter introduces a relatively simple three-dimensional continuous autonomous chaotic system, which can display complex 2- and 4-scroll attractors in simulations. Its generation and basic dynamical behaviors are briefly described.

A new chaotic system and its generation

Memristor synapse can be used to characterize the electromagnetic induction effect between two neurons that induces an action current by their membrane potential difference. This paper proposes a memristor synapse-coupled neuron network with no equilibrium, which is achieved using a memristor synapse to connect the membrane potentials of two identical three-dimensional memristive Hindmarsh–Rose neurons. Exponential synchronization is proved theoretically, and synchronous activities are discussed numerically. The theoretical and numerical results illustrate that the synchronicities of memristor synapse-coupled neuron network are related to the memristor coupling coefficient and especially related to the initial states of memristor synapse and coupling neurons. Furthermore, by constructing a ring network of memristor synapse-coupled neuron network, several types of collective behaviors including incoherent, coherent, imperfect synchronization, and chimera states are disclosed numerically, which indicate that the chimera states arisen in the ring network are dependent on the memristor coupling coefficient and sub-network coupling strength.

Memristor synapse-coupled memristive neuron network: synchronization transition and occurrence of chimera

Due to the introduction of ideal memristors, extreme multistability has been found in many autonomous memristive circuits. However, such extreme multistability has not yet been reported in a non-autonomous memristive circuit. To this end, this paper presents an improved non-autonomous memristive FitzHugh–Nagumo circuit that possesses a smooth hyperbolic tangent memductance nonlinearity, from which coexisting infinitely many attractors are obtained. By utilizing voltage–current circuit model, a three-dimensional non-autonomous dynamical model is established, based on which the initial-dependent dynamics is explored by numerical plots and extreme multistability is thereby exhibited. To confirm that the improved non-autonomous memristive circuit operates in hidden oscillating patterns, an accurate two-dimensional non-autonomous dimensionality reduction model with initial-related parameters is further built by using incremental integral transformation, upon which stability analysis and bifurcation behaviors are elaborated. Because the equilibrium state of the dimensionality reduction model is always a stable node-focus, hidden extreme multistability with coexisting infinitely many attractors is truly confirmed. Finally, PSIM circuit simulations validate the initial-related hidden dynamical behaviors.

Hidden extreme multistability and dimensionality reduction analysis for an improved non-autonomous memristive FitzHugh–Nagumo circuit

Traditional routing protocols are no longer suitable for the energy harvesting-wireless sensor networks (EH-WSN), which is powered by the energy harvested from environment instead of batteries. Rather than minimising the energy consumption and maximising the network lifetime, the main challenge in EH-WSN is to maximise its working performance under energy harvesting constraints. In this study, the authors propose a centralised power efficient routing algorithm energy harvesting genetic-based unequal clustering-optimal adaptive performance routing algorithm (EHGUC-OAPR) which contains two parts: (i) energy harvesting genetic-based unequal clustering algorithm EHGUC and (ii) optimal adaptive performance routing algorithm (OAPR). First, the base station (BS) uses EHGUC algorithm to form clusters of unequal size and select associated cluster heads, in which the clusters closer to the BS have smaller size. Then, the BS adopts OAPR algorithm to construct an optimal routing among each cluster heads. The numerical results show that EHGUC-OAPR is not only well applied to EH-WSN, but also has a great improvement in network energy balance and data delivery ratio.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-wss.2012.0117

Wenbo Liu

Papers

Hidden Bursting Firings and Bifurcation Mechanisms in Memristive Neuron Model With Threshold Electromagnetic Induction

A new chaotic system and its generation

Memristor synapse-coupled memristive neuron network: synchronization transition and occurrence of chimera

Hidden extreme multistability and dimensionality reduction analysis for an improved non-autonomous memristive FitzHugh–Nagumo circuit

Routing protocol based on genetic algorithm for energy harvesting-wireless sensor networks