In this paper, we study an HP TiO 2 memristor model with a parasitic memcapacitor, and it is shown that the parasitic element has significant effects on the volt-ampere characteristics and the ...dynamics of the memristor circuits. Further, the study shows that the pinched point on the hysteresis loop of the HP TiO 2 memristor may deviate from the origin. We also show that the memristor with a parasitic memcapacitor will eventually lose its stored flux when its power is switched off. Furthermore, in order to study the parasitic effects in circuits, we derive a simple three-element series circuit that contains an inductor, a negative resistor, and an HP TiO 2 memristor. If the parasitic memcapacitor of the memristor is considered, we observe a parasitic periodic oscillation occurred in the circuit.
This paper proposes a novel nonlinear modulating function approach for generating n-scroll chaotic attractors based on a general jerk circuit. The systematic nonlinear modulating function methodology ...developed here can arbitrarily design the swings, widths, slopes, breakpoints, equilibrium points, shapes, and even the general phase portraits of the n-scroll chaotic attractors by using the adjustable sawtooth wave, triangular wave, and transconductor wave functions. The dynamic mechanism and chaos generation condition of the general jerk circuit are further investigated by analyzing the system stability. A simple block circuit diagram, including integrator, sawtooth wave and triangular wave generators, buffer, switch linkages, and voltage-current conversion resistors, is designed for the hardware implementations of various 3-12-scroll chaotic attractors via switchings of the switch linkages. This is the first time to experimentally verify a 12-scroll chaotic attractor generated by an analog circuit. In particular, the recursive formulas of system parameters and real physical circuit parameters are rigorously derived for the hardware implementations of the n-scroll chaotic attractors. Moreover, the adjustability of the nonlinear modulating function and the rigorous recursive formulas together provide a theoretical principle for the hardware implementations of various chaotic attractors with a large number of scrolls.
In this brief, we consider the problem of blind identification in underdetermined instantaneous mixture cases, where there are more sources than sensors. A new blind identification algorithm, which ...estimates the mixing matrix in a sequential fashion, is proposed. By using the rank-1 detecting device, blind identification is reformulated as a constrained optimization problem. The identification of one column of the mixing matrix hence reduces to an optimization task for which an efficient iterative algorithm is proposed. The identification of the other columns of the mixing matrix is then carried out by a generalized eigenvalue decomposition-based deflation method. The key merit of the proposed deflation method is that it does not suffer from error accumulation. The proposed sequential blind identification algorithm provides more flexibility and better robustness than its simultaneous counterpart. Comparative simulation results demonstrate the superior performance of the proposed algorithm over the simultaneous blind identification algorithm.
The intrinsic dynamics of the Lorenz system are confined in the positive half-space with respect to the vertical axis due to a limiting threshold effect. To break such a threshold effect, a novel ...piecewise Lorenz system is introduced, equipped with a staircase function and an even symmetric piecewise-linear function. The new system is autonomous, and yet, it can generate various grid multiwing butterfly chaotic attractors without requiring any external forcing. A module-based circuit is designed for implementation, with experiments reported for verification and demonstration.
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Recently, an image encryption cryptosystem based on binary bit planes extraction and multiple chaotic maps (IEC-BPMC) was proposed, which includes two main parts: bit-level permutation for high ...4-bit planes and bit-wise XOR diffusion. Some security analyses and experimental simulations were presented to support it to resist various attacks. However, it is found that the diffusion and permutation parts can be cracked separately by the divide-and-conquer strategy due to its inherent pitfalls. Then the equivalent diffusion key and the equivalent permutation key can be recovered by the chosen-plaintext attack method. Both theoretical analysis and experimental results demonstrate that IEC-BPMC is insecure against chosen-plaintext attack with low data complexity and computational complexity. Moreover, some other security defects of IEC-BPMC are revealed. Finally, some suggestions for improvement are given to enhance the security.
This paper initiates a systematic methodology for real-time chaos-based video encryption and decryption communications on the system design and algorithm analysis. The proposed system design and ...algorithm analysis have been validated on an FPGA hardware platform via Verilog Hardware Description Language (Verilog HDL). Based on the fundamental anti-control principles of dynamical systems, a 6-D real domain chaotic system is designed, and then the corresponding Verilog HDL algorithm is developed. The proposed Verilog HDL algorithm is utilized to design a real-time chaos-based secure video communication system, with a generalized design principle derived, which is implemented on an FPGA hardware platform equipped with an XUP Virtex-II chip. Following this line, the designed working mechanism is demonstrated by hardware experiments. The security performance is tested using the TESTU01 statistical test suites, the differential analysis, and the sensitivity of key parameters mismatch. Both theoretical analysis and experimental results validate the feasibility and reliability of the proposed system.
Dictionary design as a fundamental ingredient in the Sparse-Land model is an important problem and has attracted increased attention. A proper dictionary can increase sparsity levels for sparse ...presentation and lead to better performance in the various applications. There are many effective algorithms proposed for the task of dictionary learning, such as the Method of Optimal Directions (MOD) algorithm and the K-Singular Value Decomposition (K-SVD) algorithm. The K-SVD algorithm presents performance better than the MOD algorithm, but the higher computational complexity of updating the atoms restricts its application. In this paper, we propose a new method that combines MOD with Approximate K-SVD (AK-SVD) for dictionary learning and show that it converges faster than K-SVD while obtaining better results. Experimental simulations demonstrate the efficiency of our proposed algorithm and its promising performance on the recovery of a known dictionary and dictionary learning for natural image patches. We also implement our proposed algorithm in the image denoising and evaluate its image denoising performance.
In this Letter, a novel method is developed for generating grid multi-scroll chaotic attractors using switching piecewise linear controller. First, a third-order linear system is designed to ensure ...that its unique equilibrium point belongs to a saddle-focus type with index 2 and the corresponding eigenvalues satisfy Shilnikov conditions. Then, by three different types of switching control strategies, the equilibrium point can be extended along both
xy plane and
z axis direction, so as to generate grid multi-scroll chaotic attractors. The dynamical behaviors are further analyzed. Moreover, an improved module-based circuit is designed for realizing
5
×
3
and
4
×
4
grid scroll chaotic attractors, and the experimental results are also obtained, which is consistent with the numerical simulations.
This paper introduces a novel approach called Chebyshev mapping and strongly connected topology for optimization of echo state network (ESN). To enhance the predictive performance of ESNs for time ...series data, Chebyshev mapping is employed to optimize the irregular input weight matrix. And the reservoir of the ESN is also replaced using an adjacency matrix derived from a digital chaotic system, resulting in a reservoir with strong connectivity properties. Numerical experiments are conducted on various time series datasets, including the Mackey–Glass time series, Lorenz time series and solar sunspot numbers, validating the effectiveness of the proposed optimization methods. Compared with the traditional ESNs, the optimization method proposed in this paper has higher predictive performance, and effectively reduce the reservoir’s size and model complexity.
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