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— In this article, a study on increasing security of audio data encryption with single and double dimension discrete-time chaotic systems was carried out and application and security analyses were executed. Audio data samples of both mono and stereo types were encrypted. In the application here, single and double dimension discrete-time chaotic systems were used. In order to enhance security during encryption, a different method was applied by also using a non-linear function. In the chaos based application realized with the method developed, analyses results were achieved with common security analyses such as key space, key sensitivity, chaos effect and histogram. Several examinations on the safety of chaotic systems in the application were carried out with these analyses results

In this paper, a multiscroll snap oscillator with hyperbolic tangent function is proposed. There is no limitation in the number of scrolls and it can be increased by proper choice of a specific function. The Lyapunov exponents of the proposed system are obtained to testify the chaotic behavior of the system. Fractional order multiscroll system is derived from its integer order model by using the Adams–Bashforth–Moulton algorithm. A new scheme is applied in order to investigate the synchronization of the multiscroll systems. The main objective of the paper is to propose a multiscroll attractor and show that the number of scrolls can be controlled by the only nonlinear function. Such systems are less investigated in the literatures and has many real time applications like image and voice encryption, random number generators, chaos based communication systems and so on.

Simple dynamical systems are of interest always. In this paper, we propose a simple jerk system with one exponential nonlinearity. Dynamical properties of the proposed system are investigated. To show the practical realizability of the proposed system we implement the exponential jerk system using off the shelf components. Fractional order and time delays are considered as complex analysis patterns of nonlinear systems. We investigate the fractional order time delayed exponential jerk system. For numerical analysis we use the modified Adomian Decomposition Method. To show the engineering importance of the proposed system, we derive a pseudo random number generator based on it.Various test results are presented to show the randomness of the system.

Hyperjerk systems have received significant interest in the literature because of their simple structure and complex dynamical properties. This work presents a new chaotic hyperjerk system having two exponential nonlinearities. Dynamical properties of the chaotic hyperjerk system are discovered through equilibrium point analysis, bifurcation diagram, dissipativity and Lyapunov exponents. Moreover, an adaptive backstepping controller is designed for the synchronization of the chaotic hyperjerk system. Also, a real circuit of the chaotic hyperjerk system has been carried out to show the feasibility of the theoretical hyperjerk model. The chaotic hyperjerk system can also be useful in scientific fields such as Random Number Generators (RNGs), data security, data hiding, etc. In this work, three implementations of the chaotic hyperjerk system, viz. RNG, image encryption and sound steganography have been performed by using complex dynamics characteristics of the system.

We introduce and investigate a four-dimensional hidden hyperchaotic system without equilibria, which is obtained by augmenting the three-dimensional self-exciting homopolar disc dynamo due to Moffatt with an additional control variable. Synchronization of two such coupled disc dynamo models is investigated by active control and sliding mode control methods. Numerical integrations show that sliding mode control provides a better synchronization in time but causes chattering. The solution is obtained by switching to active control when the synchronization errors become very small. In addition, the electronic circuit of the four-dimensional hyperchaotic system has been realized in ORCAD-PSpice and on the oscilloscope by amplitude values, verifying the results from the numerical experiments. National Natural Science Foundation of China (NSFC) - 11561069 Guangxi Natural Science Foundation of China - 2016GXNSFBA380170 Scientific Research Foundation of the Higher Education Institutions of Guangxi Province of China - KY2016YB364 Open Foundation for Guangxi Colleges and Universities Key Lab of Complex System Optimization and Big Data Processing - 2016CSOBDP0003 - 2016CSOBDP0202 Sakarya Üniversitesi - 201609-00008