15,431 research outputs found
Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics
This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provide
Hidden attractors in fundamental problems and engineering models
Recently a concept of self-excited and hidden attractors was suggested: an
attractor is called a self-excited attractor if its basin of attraction
overlaps with neighborhood of an equilibrium, otherwise it is called a hidden
attractor. For example, hidden attractors are attractors in systems with no
equilibria or with only one stable equilibrium (a special case of
multistability and coexistence of attractors). While coexisting self-excited
attractors can be found using the standard computational procedure, there is no
standard way of predicting the existence or coexistence of hidden attractors in
a system. In this plenary survey lecture the concept of self-excited and hidden
attractors is discussed, and various corresponding examples of self-excited and
hidden attractors are considered
Fully CMOS Memristor Based Chaotic Circuit
This paper demonstrates the design of a fully CMOS chaotic circuit consisting of only DDCC based memristor and inductance simulator. Our design is composed of these active blocks using CMOS 0.18 ”m process technology with symmetric ±1.25 V supply voltages. A new single DDCC+ based topology is used as the inductance simulator. Simulation results verify that the design proposed satisfies both memristor properties and the chaotic behavior of the circuit. Simulations performed illustrate the success of the proposed design for the realization of CMOS based chaotic applications
Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems
Traditionally, chaotic systems are built on the domain of infinite precision
in mathematics. However, the quantization is inevitable for any digital
devices, which causes dynamical degradation. To cope with this problem, many
methods were proposed, such as perturbing chaotic states and cascading multiple
chaotic systems. This paper aims at developing a novel methodology to design
the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite
precision. The proposed system is based on the chaos generation strategy
controlled by random sequences. It is proven to satisfy the Devaney's
definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The
application of HDDCS in image encryption is demonstrated via FPGA platform. As
each operation of HDDCS is executed in the same fixed precision, no
quantization loss occurs. Therefore, it provides a perfect solution to the
dynamical degradation of digital chaos.Comment: 12 page
Yet Another Pseudorandom Number Generator
We propose a novel pseudorandom number generator based on R\"ossler attractor
and bent Boolean function. We estimated the output bits properties by number of
statistical tests. The results of the cryptanalysis show that the new
pseudorandom number generation scheme provides a high level of data security.Comment: 5 pages, 7 figures; to be published in International Journal of
Electronics and Telecommunications, vol.63, no.
- âŠ