Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication

2022 ◽  
Author(s):  
Wenhao Yan ◽  
Zijing Jiang ◽  
Qun Ding
Keyword(s):  
Fixed Points ◽  
Discrete Time ◽  
Dynamic Characteristics ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Two Dimensional ◽  
Initial State ◽  
One Dimensional ◽  
Backward Euler ◽  
Short Period

Abstract The physical implementation of continuoustime memristor makes it widely used in chaotic circuits, whereas discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize TiO2 memristor model, and the discretized model also meets the three fingerprinter characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling the proposed TiO2 memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete TiO2 memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication.

Novel discrete chaotic system via fractal transformation and its DSP implementation

2020 ◽  
pp. 2050429
Author(s):  
Shengqiu Dai ◽  
Kehui Sun ◽  
Wei Ai ◽  
Yuexi Peng
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Map ◽  
Digital Circuit ◽  
Distribution Characteristics ◽  
Two Dimensional ◽  
Mathematical Operation ◽  
One Dimensional ◽  
Spectrum Distribution ◽  
Application Prospects

Designing a discrete chaotic system via fractal transformation has become a new method for engineering applications. This method generates new discrete chaotic system through external mechanisms, instead of the traditional way of internal mechanisms. The way of building novel discrete chaotic system is enriched by fractal and mathematical operation. Taking one-dimensional ICMIC map and two-dimensional Hénon map as the seed maps, dynamics of the generated chaotic map is analyzed by bifurcations, complexity and spectrum distribution characteristics. The results show that the new discrete chaotic map has the advantages in complexity and distribution in the parameter space. Finally, the digital circuit of fractal chaotic system is implemented based on DSP technique. The feasibility of the circuit is verified. Therefore, it has good application prospects in secure communication.

A general method for projective-lag synchronization of heterogeneous chaotic maps with different dimensions

2021 ◽  
pp. 107754632110264
Author(s):  
Cun-Fang Feng ◽  
Hai-Jun Yang ◽  
Cai Zhou
Keyword(s):  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Lag Synchronization ◽  
Different Dimensions ◽  
Projective Lag Synchronization ◽  
General Method

Projective-lag synchronization of complex systems has attracted much attention in the past two decades. However, the majority of previous studies concentrated on continuous-time chaotic systems or discrete-time chaotic systems with the same dimensions. In our present study, a general method for projective-lag synchronization of different discrete-time chaotic systems characterized with different dimensions is first demonstrated. On the basis of stability theory of discrete-time dynamical systems and Lyapunov stability theory, general controllers are designed by using the active control method. The method could achieve projective-lag synchronization in both cases: [Formula: see text] and [Formula: see text]. The effectiveness and feasibility of the proposed method is demonstrated by the projective-lag synchronization between two-dimensional Lorenz discrete-time system and three-dimensional Stefanski map, as well as between the three-dimensional generalized Hénon map and the two-dimensional quadratic map, respectively.

GENERATION OF PSEUDO-CHAOTIC SEQUENCES

1994 ◽  
Vol 04 (03) ◽  
pp. 709-713 ◽  
Author(s):  
T. KILIAS
Keyword(s):  
Discrete Time ◽  
Spectral Properties ◽  
Chaotic Systems ◽  
Chaotic Maps ◽  
Maximum Length ◽  
Shift Register ◽  
One Dimensional ◽  
Chaotic Sequences ◽  
Random Signals

This paper deals with the spectral properties of pseudo-random signals generated in maximum-length shift registers. It is shown that infinitely long registers are comparable in behavior with one-dimensional discrete-time chaotic maps. Therefore the theory, results and tools developed for chaotic systems can be applied to the design of the spectral properties of maximum-length shift register sequences.

scholarly journals CHAOS ENTANGLEMENT: A NEW APPROACH TO GENERATE CHAOS

2013 ◽  
Vol 23 (05) ◽  
pp. 1330014 ◽  
Author(s):  
HONGTAO ZHANG ◽  
XINZHI LIU ◽  
XUEMIN SHEN ◽  
JUN LIU
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Complex Dynamics ◽  
Saddle Points ◽  
Dynamical Analysis ◽  
Chaotic Attractors ◽  
New Approach ◽  
One Dimensional ◽  
Linear Subsystem ◽  
Stable Linear

A new approach to generate chaotic phenomenon, called chaos entanglement, is proposed in this paper. The basic principle is to entangle two or multiple stable linear subsystems by entanglement functions to form an artificial chaotic system such that each of them evolves in a chaotic manner. Firstly, a new attractor, entangling a two-dimensional linear subsystem and a one-dimensional one by sine function, is presented as an example. Dynamical analysis shows that both entangled subsystems are bounded and all equilibra are unstable saddle points when chaos entanglement is achieved. Also, numerical computation shows that this system has one positive Lyapunov exponent, which implies chaos. Furthermore, two conditions are given to achieve chaos entanglement. Along this way, by different linear subsystems and different entanglement functions, a variety of novel chaotic attractors have been created and abundant complex dynamics are exhibited. Our discovery indicates that it is not difficult any more to construct new artificial chaotic systems/networks for engineering applications such as chaos-based secure communication. Finally, a possible circuit is given to realize these new chaotic attractors.

Subcritical Neimark–Sacker bifurcation and hybrid control in a discrete-time Phytoplankton–Zooplankton model

2021 ◽  
Author(s):  
A. Q. Khan ◽  
M. B. Javaid
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Discrete Time ◽  
Control Strategy ◽  
Hybrid Control ◽  
Dynamical Behavior ◽  
Flip Bifurcation ◽  
Two Dimensional ◽  
Theoretical Results

In this paper, we explore the local dynamical behavior with different topological classifications around fixed points, Neimark–Sacker bifurcation and hybrid control in the discrete-time Phytoplankton–Zooplankton model. More precisely, we have investigated the local dynamical behavior with different topological classifications around trivial, semitrivial and interior fixed points of the two-dimensional Phytoplankton–Zooplankton model, respectively. The existence of possible bifurcations around fixed points is also investigated, and it is proved that there exists no flip bifurcation around trivial and semitrivial fixed points but around interior fixed point, the model undergoes Neimark–Sacker bifurcation only. Moreover, hybrid control strategy is utilized for controlling Neimark–Sacker bifurcation in the Phytoplankton–Zooplankton model. Lastly, theoretical results are verified numerically.

Connecting Curves as a Tool to Localize Hidden Attractors in a New Chaotic Hyperjerk System with No Equilibria

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Nafise Naseri ◽  
Sivabalan Ambigapathy ◽  
Mohadeseh Shafiei Kafraj ◽  
Farnaz Ghassemi ◽  
Karthikeyan Rajagopal ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Fixed Points ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Chaotic Attractors ◽  
Hidden Attractors ◽  
One Dimensional ◽  
Pass Through ◽  
Hyperjerk System

Localizing hidden attractors of chaotic systems is practically and theoretically important. Differing from self-excited attractors, hidden ones do not have any equilibria on the boundaries of their basin of attraction. This characteristic makes hidden attractors hard to localize. Some theoretical and numerical methods have been developed to recognize these attractors, yet the problem remains highly uncertain. For this purpose, the theory of connecting curves is utilized in this work. These curves are one-dimensional set-points that describe the structure of chaotic attractors even in the absence of zero-dimensional fixed-points. In this study, a new four-dimensional chaotic system with hidden attractors is presented. Despite the controversial idea of connecting curves that pass through fixed-points, the connecting curves of a system with no equilibria are considered. This analysis confirms that connecting curves provide more critical information about attractors even if they are hidden.

scholarly journals Synchronization of fractional–order discrete–time chaotic systems by an exact delayed state reconstructor: Application to secure communication

2019 ◽  
Vol 29 (1) ◽  
pp. 179-194 ◽  
Author(s):  
Said Djennoune ◽  
Maamar Bettayeb ◽  
Ubaid Muhsen Al-Saggaf
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Data Communication ◽  
Speech Communication ◽  
Discrete Time Systems ◽  
New Concepts ◽  
True State ◽  
Time Systems

Abstract This paper deals with the synchronization of fractional-order chaotic discrete-time systems. First, some new concepts regarding the output-memory observability of non-linear fractional-order discrete-time systems are developed. A rank criterion for output-memory observability is derived. Second, a dead-beat observer which recovers exactly the true state system from the knowledge of a finite number of delayed inputs and delayed outputs is proposed. The case of the presence of an unknown input is also studied. Third, secure data communication based on a generalized fractional-order Hénon map is proposed. Numerical simulations and application to secure speech communication are presented to show the efficiency of the proposed approach.

DISCRETE-TIME CHAOTIC SYSTEMS: APPLICATIONS IN SECURE COMMUNICATIONS

2000 ◽  
Vol 10 (09) ◽  
pp. 2193-2206 ◽  
Author(s):  
KUANG-YOW LIAN ◽  
TUNG-SHENG CHIANG ◽  
PETER LIU
Keyword(s):  
Kalman Filter ◽  
Numerical Simulations ◽  
Extended Kalman Filter ◽  
Discrete Time ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Error Rates ◽  
Alternative Methods ◽  
Secure Communications ◽  
Binary Signal

The general design for dead-beat and asymptotic synchronizers for a large class of discrete-time chaotic systems is proposed. According to whether the form of the transmitter output (drive signal) is linear, nonlinear or the sum of two, different system structures for synchronization discussions are held. Secure communications is then applied taking into consideration to which state in the transmitter masks the message. Examples of different secure communication schemes are discussed, with a comparison given of the various schemes based on the performance of the receivers ability to recover the message. To accomodate the uncertainty existing in the transmitter parameters, an extended Kalman filter (EKF) algorithm is utilized to estimate both the parameters and states when the message is already embedded. To overcome the problem of high error rates of recovered messages while simultaneously estimating parameters, two alternative methods, namely linear output scheme and indirect scheme, are presented to improve the performance. Numerical simulations for secure communications illustrate a binary signal as the message is recovered and recognizable at the receiver's end.

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