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This paper proposes a generalized modified chaotic transition map with three independent parameters. A hardware speech encryption scheme utilizing this map along with a bit permutation network is presented. While the transition map’s generalization introduces additional parameters, the modification enhances its chaotic properties and overcomes the finite range of the control parameter and dynamical...
In the recent decades, applications of chaotic systems have flourished in various fields. Hence, there is an increasing demand on generalized, modified and novel chaotic systems. In this paper, we combine the general equation of jerk-based chaotic systems with simple scaled discrete chaotic maps. Numerical simulations of the properties of two systems, each with four control parameters, are presented...
The tent map is a piece-wise linear one-dimensional discrete map which could be implemented easily. In this paper, a signed system parameter is allowed leading to the appearance of bidirectional bifurcations. A set of proposed tent maps with different sign variations and a signed parameter are investigated where the conventional map is a special case. The proposed maps exhibit period doubling as a...
In this paper, a generalized scheme for synchronizing a fractional order chaotic system with another one or with a linear combination of two other fractional order chaotic systems is presented. Static (time-independent) or dynamic (time-dependent) synchronization that could generate multiple scaled versions of the response is discussed for some fractional order continuous chaotic systems based on...
This paper discusses the continuous effect of fractional order parameter on two chaotic systems. Switched synchronization of three different fractional order chaotic systems is presented as an extension for synchronizing two different systems using active control. The proposed technique, which is based on the switching parameters and the scaling factors that control the choices of master and slave...
The discrete tent map is one of the most famous discrete chaotic maps that has widely-spread applications. This paper investigates a set of four generalized tent maps where the conventional map is a special case. The proposed maps have extra degrees of freedom which provide different chaotic characteristics and increase the design flexibility required for many applications. Mathematical analyses for...
Nonlinear analysis and chaos have many applications in communications, cryptography, and many other fields. In this work, we aim to bridge the gap between mathematical analysis of generalized 1D discrete chaotic maps and their implementation on digital platforms. We propose several variations and generalizations on the logistic and tent maps and employ the power function z = xy in a general map that...
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