scholarly journals Design of Initial Value Control for Modified Lorenz-Stenflo System

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Yuan-Long Wu ◽  
Cheng-Hsiung Yang ◽  
Chang-Hsi Wu
Keyword(s):  
Circuit Design ◽  
Chaotic Systems ◽  
Analog Circuit ◽  
Initial Conditions ◽  
Control Circuit ◽  
Initial Value ◽  
Sensitivity To Initial Conditions

For the sake of complexity, unpredictability, and exceeding sensitivity to initial conditions in the chaotic systems, there were many studies for information encryption of chaotic systems in recent years. Enhancing the security in information encryption of chaotic systems, an initial value control circuit for chaotic systems is proposed in this paper. By way of changing the initial value, we can change the behavior of chaotic systems and also change the key of information encryption. An analog circuit is implemented to verify the initial value control circuit design.

A New Image Encryption Scheme Using Dual Chaotic Map Synchronization

2020 ◽  
Vol 18 (1) ◽  
Keyword(s):  
Image Encryption ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Chaotic Map ◽  
Security Applications ◽  
The Common ◽  
And Diffusion ◽  
Confusion And Diffusion ◽  
Sensitivity To Initial Conditions ◽  
Diffusion Properties

Chaotic systems behavior attracts many researchers in the field of image encryption. The major advantage of using chaos as the basis for developing a crypto-system is due to its sensitivity to initial conditions and parameter tunning as well as the random-like behavior which resembles the main ingredients of a good cipher namely the confusion and diffusion properties. In this article, we present a new scheme based on the synchronization of dual chaotic systems namely Lorenz and Chen chaotic systems and prove that those chaotic maps can be completely synchronized with other under suitable conditions and specific parameters that make a new addition to the chaotic based encryption systems. This addition provides a master-slave configuration that is utilized to construct the proposed dual synchronized chaos-based cipher scheme. The common security analyses are performed to validate the effectiveness of the proposed scheme. Based on all experiments and analyses, we can conclude that this scheme is secure, efficient, robust, reliable, and can be directly applied successfully for many practical security applications in insecure network channels such as the Internet

scholarly journals Sources of uncertainty in deterministic dynamics: an informal overview

2011 ◽  
Vol 369 (1956) ◽  
pp. 4705-4729 ◽  
Author(s):  
Ian Stewart
Keyword(s):  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Sources Of Uncertainty ◽  
Deterministic Systems ◽  
Coin Tossing ◽  
Random Switching ◽  
Butterfly Effect ◽  
Basin Boundaries ◽  
Sensitivity To Initial Conditions

The discovery of chaotic dynamics implies that deterministic systems may not be predictable in any meaningful sense. The best-known source of unpredictability is sensitivity to initial conditions (popularly known as the butterfly effect), in which small errors or disturbances grow exponentially. However, there are many other sources of uncertainty in nonlinear dynamics. We provide an informal overview of some of these, with an emphasis on the underlying geometry in phase space. The main topics are the butterfly effect, uncertainty in initial conditions in non-chaotic systems, such as coin tossing, heteroclinic connections leading to apparently random switching between states, topological complexity of basin boundaries, bifurcations (popularly known as tipping points) and collisions of chaotic attractors. We briefly discuss possible ways to detect, exploit or mitigate these effects. The paper is intended for non-specialists.

Control Lorenz System with Vibration Estimation with Averaging Method

2010 ◽  
Vol 43 ◽  
pp. 36-39
Author(s):  
Chun Zhou
Keyword(s):  
Chaotic Systems ◽  
Inverted Pendulum ◽  
Lorenz System ◽  
Stable Equilibrium ◽  
Averaging Method ◽  
Control Method ◽  
Initial Conditions ◽  
Vibrational Control ◽  
Extreme Sensitivity ◽  
Sensitivity To Initial Conditions

The vibrational control theory stems from the well-known of stabilization of the upper unstable equilibrium position of the inverted pendulum having suspension point vibration along the vertical line with amplitude as small as desired and a frequency reason high. Chaotic phenomena have been found in many nonlinear systems including continuous time and discrete time. The chaotic systems are characterized by their extreme sensitivity to initial conditions, nonperiodic and boundary. The trajectories start even from close initial states will diverge from each other at an exponential rate as time goes. The vibrational control method was applied to Lorenz system. The effect of the control can be estimated with the APAZ method. It was showed that vibrational control brought the controlled Lorenz system to stable equilibrium with appropriate parameters. Numerical simulation demonstrated validity of the proposed method.

A Fractional-Order Hyperchaotic System and its Circuit Implement

2014 ◽  
Vol 701-702 ◽  
pp. 1143-1147
Author(s):  
Qi Li Wang
Keyword(s):  
Fractional Order ◽  
Strange Attractor ◽  
Analog Circuit ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Order System ◽  
Hyperchaotic System ◽  
Dynamical Properties ◽  
Simulation Results ◽  
Sensitivity To Initial Conditions

A fractional-order hyperchaotic system was proposed and some basic dynamical properties were investigated to show chaotic behavior. These properties include instability of equilibria, sensitivity to initial conditions, strange attractor, Lyapunov exponents, and bifurcation. The fractional-order system presents hyperchaos, chaos, and periodic behavior when the parameters vary continuously. Then, an analog circuit is designed onMultisim 11and the Multisim results are agreed with the simulation results.

The Features of Chaos

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Phase Space ◽  
Lyapunov Exponent ◽  
Correlation Dimension ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Average Rate ◽  
Quantitative Measure ◽  
Fractal Dimensions ◽  
Recurrence Plot ◽  
Sensitivity To Initial Conditions

In this chapter we introduce the features of Chaotic systems. We describe “sensitivity to initial conditions” and its quantitative measure, the Lyapunov exponent, which reflect the average rate of divergence (if any) between two neighboring trajectories. We describe the dynamic “strangeness” of the system. Which has its counterpart in the “strangeness” of the attractor's geometry and concerns with the texture woven by the system in phase space. Fractal dimensions are measures of such strange geometries and they are here described. The concept of recurrence is introduced and the recurrence plot is described, and code provided to generate it. The correlation dimension is addressed and the R code to compute is listed and detailed. Poincare map is introduced and applied to the study of the damped, driven pendulum.

Whale optimization based synchronization and control of two identical fractional order financial chaotic systems

2021 ◽  
pp. 1-14
Author(s):  
Sangeeta Gupta ◽  
Pragya Varshney ◽  
Smriti Srivastava
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Optimization Techniques ◽  
Complete Synchronization ◽  
Whale Optimization ◽  
Parameter Perturbations ◽  
And Control ◽  
Method Analysis ◽  
Sensitivity To Initial Conditions

This paper proposes a scheme to synchronize fractional order chaotic systems employing fractional PID controller. The parameters of FOPID are tuned using Swarm based optimization techniques, viz.: Whale optimization algorithm and Particle swarm optimization techniques. To assert the complete synchronization, master-slave method has been implemented. Chaotic systems are highly dependent upon initial conditions and parameter perturbations. Therefore, taking these properties into consideration, synchronization of two identical fractional order financial chaotic systems is performed with distinct initial conditions. To show the efficacy of the proposed method, analysis is performed for orders between 0 to 1, and also for sensitivity to initial conditions.

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