In this paper, a novel approach is developed for multi-images encryption and decryption by using single discrete time chaotic system and anti-control methodology. The field programmable gate array ...(FPGA) embedded implementations are demonstrated, and the corresponding NIST safety performance test results are also given.
The rheological and textural properties of κ-carrageenan (CAR) and konjac glucomannan (KGM) with definite deacetylation degree (DD) mixed system in the presence of potassium chloride (KCl) were ...investigated to study the influence of deacetylation degree on KGM, CAR and KCl mixed system. The results revealed that the zero-shear viscosities of the mixed sol system increased firstly and then decreased with the gradual increase of DD. Besides, the sols had the capability of being transformed into irreversible gel by heating them at 80 °C for 30 min and then cooling to room temperature. The DD of KGM did have impacts on the characteristics of the ensuing hydrogels. That is, the mixed gels showed an initial increase and ensuing decrease in gel strength over DD, reaching the maximum with a DD of 21.07%. Overall, by controlling the deacetylation degree of KGM, the gel behaviors of the mixed system can be regulated.
Display omitted
•Deacetylated KGM was prepared by the method of heterogeneous deacetylation reaction.•Deacetylated KGM/CAR/KCl mixed systems were composited as the research object.•The effect of deacetylation degree of KGM on the properties of mixture was investigated.
► This article develops a new method for designing general continuous-time autonomous chaotic systems. ► The new design method is universal, based on Lyapunov exponent placement. ► This self-unified ...method is semi-analytical with guidelines for design and implementation. ► This new method is mathematically rigorous. ► This new method guarantees the resulting system be chaotic in the sense of Shilnikov.
Based on two basic characteristics of continuous-time autonomous chaotic systems, namely being globally bounded while having a positive Lyapunov exponent, this paper develops a universal and practical anti-control approach to design a general continuous-time autonomous chaotic system via Lyapunov exponent placement. This self-unified approach is verified by mathematical analysis and validated by several typical systems designs with simulations. Compared to the common trial-and-error methods, this approach is semi-analytical with feasible guidelines for design and implementation. Finally, using the Shilnikov criteria, it is proved that the new approach yields a heteroclinic orbit in a three-dimensional autonomous system, therefore the resulting system is indeed chaotic in the sense of Shilnikov.
The security analysis of the existing chaotic image encryption algorithm is mainly for the algorithm whose secret keys are independent of plaintext, while a few cryptanalyses on plaintext-related ...scheme are released. This paper analyzes the security of a chaotic encryption algorithm related to the sum of plaintext pixel value (SPPV). It is found that for all plaintexts with the same SPPV, the chaotic sequences used for encryption are identical. Accordingly, there exist a series of equivalent keys corresponding to the different SPPVs, a codebook attack method to crack this type of encryption algorithm is proposed. Since the SPPV is predictable, limited in number and reconfigurable, the chosen-plaintext attack is adopted to analyze the plaintext with all possible SPPVs. And the corresponding equivalent keys are calculated, respectively. These equivalent keys corresponding to SPPV finally form a complete codebook for cracking the original encryption scheme. The research result shows that any encryption algorithm related to SPPV can be cracked by the codebook attack method proposed in this paper. Therefore, the method proposed in this paper owns certain universal applicability. Theoretical analysis and experimental results prove the feasibility of this method.
In this paper, we introduce a memristor model and a meminductor model and design the corresponding emulator circuits for imitating their characteristics. By employing the two models, we propose a ...very simple chaotic circuit that contains only three elements in parallel: a memristor, a meminductor and a linear passive capacitor. The circuit is very simple, but has very abundant dynamical behaviors, including line equilibrium set, bursting, coexisting attractors, transient chaos, transient period and intermittency. Furthermore, we replace the memristor and meminductor with their corresponding emulators in the proposed circuit to make a hardware experiment, which illustrates the validity of the theoretical analysis.
This paper aims to refine and expand the theoretical and application framework of higher-dimensional digital chaotic system (HDDCS). Topological mixing for HDDCS is strictly proved theoretically at ...first. Topological mixing implies Devaney's definition of chaos in a compact space, but not vice versa. Therefore, the proof of topological mixing promotes the theoretical research of HDDCS. Then, a general design method for constructing HDDCS via loop-state contraction algorithm is given. The construction of the iterative function uncontrolled by random sequences (hereafter called iterative function) is the starting point of this research. On this basis, this paper put forward a general design method to solve the construction problem of HDDCS, and several examples illustrate the effectiveness and feasibility of this method. The adjacency matrix corresponding to the designed HDDCS is used to construct the chaotic Echo State Network (ESN) for predicting Mackey-Glass time series. Compared with other ESNs, the chaotic ESN has better prediction performance and is able to accurately predict a much longer period of time.
There exist two different types of equilibrium points in 3-D autonomous systems, named as saddle foci of index 1 and index 2, which are crucial for chaos generation. Although saddle foci of index 2 ...have been usually applied for creating double-scroll or double-wing chaotic attractors, saddle foci of index 1 are further considered for chaos generation in this paper. A novel approach for constructing chaotic systems is investigated by applying the switching control strategy and yielding a heteroclinic loop which connects two saddle foci of index 1. A basic 3-D linear system with an arbitrary normal direction of the eigenplane, possessing a saddle focus of index 1 whose corresponding eigenvalues satisfy the Shil'nikov inequality, is first introduced. Then a heteroclinic loop connecting two saddle foci of index 1 will be formed by applying the switching control strategy to the basic 3-D linear system. The heteroclinic loop consists of an unstable manifold, a stable manifold, and a heteroclinic point. Under the necessary conditions for forming the heteroclinic loop, the intended two-segmented piecewise linear system which exhibits the chaotic behavior in the sense of the Smale horseshoe can be finally constructed. An illustrative example is given, confirming the effectiveness of the proposed method.
Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, the quantization is inevitable for any digital devices, which causes dynamical degradation. To ...cope with this problem, many methods were proposed, such as perturbing chaotic states and cascading multiple chaotic systems. This paper aims at developing a novel methodology to design the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite precision. The proposed system is based on the chaos generation strategy controlled by random sequences. It is proven to satisfy the Devaney's definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The application of HDDCS in image encryption is demonstrated via FPGA platform. As each operation of HDDCS is executed in the same fixed precision, no quantization loss occurs. Therefore, it provides a perfect solution to the dynamical degradation of digital chaos.
A number of important applications would benefit from the introduction of locally-active memristors, which is defined to be any memristor that exhibits negative differential memristance for at least ...a voltage or a current applied to the memristor. Two leading examples are emerging nonvolatile memory based on memristor-based crossbar array architectures, and neural networks that exhibit improved computational complexity when operated at the edge of chaos. In this paper, a novel locally-active memristor model is presented for exploring the nonvolatile and switching mechanism of the memristor and the influence of local activity on the complexity of nonlinear circuits. We find that the memristor possesses three locally-active regions in its DC
V
–
I
plot and two asymptotically stable states (equilibrium points) on its power-off plot (POP) where voltage
v
=
0
, implying that the memristor is bistable, which can be used as a nonvolatile binary memory or binary switch. We also find the mechanism and the rule of switching between the two stable states by applying a single square voltage pulse of appropriate pulse width and pulse amplitude. We show that it is always possible to switch from one stable state to another of the memristor with an appropriate pulse amplitude and a pulse width, and that there is a trade-off between the voltage pulse amplitude and the pulse width for the faster switching between the two equilibrium points. We also show that fast switching between the two states is possible by using a periodic bipolar narrow pulse sequence. Local activity depends on the capability of a memristor circuit to amplify infinitesimal fluctuations in energy. Based on this principle, we designed a simplest chaotic oscillator that utilizes only three components in parallel: the proposed locally-active memristor, a linear capacitor and an inductor, which can oscillate around an equilibrium point located on its DC
V
–
I
plot. Its dynamic characteristics are verified by theoretical analyses, simulations and DSP experiments.
PDF
