Suppression of pattern complexity by discrete-space state feedback with equal intervals

An image encryption scheme based on the MLNCML system using DNA sequences

An image encryption scheme based on new spatiotemporal chaos

Intelligent home products have serious information security risks, threatening the privacy of users. In this paper, a method of password protection using hyper-chaos based one-way hash function and secure information transmission method based on spatiotemporal chaos are proposed. The proposed method creates a unidirectional hash function using the delay induced hyper-chaotic system and the key stream iteration to protect user password and to realize user authentication. At the same time, the chaotic time series generated by the one way coupled map lattice system is used to encrypt the plaintext information for the data secure communication, which increases the security of the intelligent home system. An intelligent home system prototype is built based on a Zigbee network, cloud server, and Android system.

A computational approach is proposed to solve the minimum norm and/or robust pole assignment problem for linear periodic discrete-time systems. The proposed approach uses a periodic Sylvester equation based parametrization of the periodic pole assignment problem and exploits the non-uniqueness of the problem by imposing conditions on the norm of the resulting periodic state feedback and/or on the condition numbers of the periodic eigenvector matrices of the closed-loop system. The solution method relies on using gradient search methods on suitably defined cost functions. Explicit expression of the gradients of cost functions are derived and the efficient evaluation of the cost functions and gradients is discussed. Numerical examples illustrate the effectiveness of the proposed approach.

This paper considers pole assignment and robust pole assignment problems for discrete-time linear periodic systems by using linear periodic state feedback. The monodromy matrix of the closed-loop system is represented in a special form. By combining this special form with our recent result on solutions to a class of generalized Sylvester matrix equations, a complete parametric approach for pole assignment via periodic state feedback is proposed. The free parameters existing in the solutions to pole assignment are further used to achieve robustness performances. The robust pole assignment problem is converted into a nonconvex optimization problem. Numerical examples illustrate the effectiveness of the proposed approaches.

As a kind of spatiotemporal chaos, coupled map lattice (CML) is widely applied into image encryption because of its advantages of more complex dynamical behavior and lower computational overhead. Firstly, this paper proposed a novel spatiotemporal chaos model (MCML) by mixing Logistic, Sine and Tent maps into CML map together. Beyond that, we also change the structure of CML and the coupling method in different lattices. Bifurcation diagram, Lyapunov exponents and NIST test are employed to measure the chaotic behaviors of the MCML system. Secondly, by applying MCML chaos, we design a new key binding and distribution rule, the improved diffusion scheme to encrypt image. Furthermore, the novel bit Z-scan scrambling method also be used to enhance the security of the encryption scheme. Finally, a large number of experimental results prove that our proposed scheme is suitable for image encryption and has high security against common attacks.

A coupled map lattice system is perturbed by a local injection. The system response to the external excitation is investigated. We find a phase transition from local response to a global response. As global response functions the motions of the sites far from the forced site show critical on-off intermittency. The implication of the global response to the physical transportation behavior is addressed.

Garca Guirao and Lampart (J Math Chem 48:66–71, 2010; J Math Chem 48:159–164, 2010) said that for non-zero couplings constant, the lattice dynamical system is more complicated. Motivated by this, in this paper, we prove that this coupled map lattice system is Li–Yorke chaotic for coupling constant \({0 < \epsilon <1 }\) .

This paper proposes a new spatiotemporal chaos model, which is a logistic-dynamic coupled logistic map lattice (LDCML). Through a large number of simulation experiments and theoretical analysis, it can be proved that a chaotic region has the larger parameter space, and the system is more chaotic compared with traditional CML by the introduction of a dynamic coupled method, which is more suitable for chaotic encryption and secure communications. So, this paper presents a bit-level adaptive image encryption algorithm based on this system, and further demonstrates the good chaos of the system from the aspect of encryption performance.

We study the direction dependence of the density of directional entropy in lattice dynamical systems. We show that if the dynamics is homogeneous and continuous, then this density does not depend on the direction in space–time. By using symbolic dynamics we derive formulae for the density for weakly coupled hyperbolic maps. As a corollary, we present examples where this density actually depends on the direction, provided that individual subsystems are sufficiently different.

In this paper, the stable control of spatiotemporal chaos in coupled map lattices is realized by state feedback method. The feedback mode can be either delayed or without delay. The control mode can be either continuous or pulsate. The numerical simulation results demonstrate that this method is an effective one.

The onset of spatiotemporal chaos in coupled map lattice (CML) with a new coupling scheme called accumulated CML is studied in this paper. A rigorous proof of the existence of chaos in the sense of Li–Yorke is presented. Also the range of the coupling strength in which global synchronization can be obtained is calculated by stability analysis of the synchronized state. Finally, the positivity of Lyapunov exponents confirms the existence of chaos.

The coupled map lattices (CML) is a spatiotemporal chaotic system with complex dynamic behavior. In this paper, we propose a spatiotemporal chaotic system with a novel pseudo-random coupling method based on elementary cellular automata (ECA), and introduce different perturbations into lattices in each iteration according to ECA. We investigate the spatiotemporal dynamic properties and chaotic behaviors of the proposed system such as bifurcation diagrams, Kolmogorov Sinai entropy, and uniformity. Moreover, the randomness of sequences generated by the proposed system and the correlation between any two lattices are discussed. Theory analyses and simulations indicate that the new system has better performance in complexity, ergodic and unpredictability than other CML systems such as adjacent CML and nonlinear CML based on fractional order logistic equation, etc. Furthermore, the correlation coefficient between any two lattices in the proposed system is significantly lower than other systems, and another advantage of the proposed system is utilizing the output of ECA to perturb the chaotic system which can effectively alleviate the dynamical degradation in digital system. The excellent performance of the proposed system demonstrates that it has great potential for crypto-system.

Emergence of order in dynamical phases in coupled fractional gauss map

We present an experimental evidence for spatiotemporal stability of a real one-way open coupled map lattice implemented by electronic circuits. Furthermore, it is shown that the decentralized delayed feedback control method can suppress the spatial instability and the spatiotemporal chaos in the coupled map lattice circuits.