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

Nonlinear Resistor with Polynomial AV Characteristics and Its Application in Chaotic Oscillator

This paper shows the realization of two terminal devices with an arbitrary polynomial nonlinearity up to the fifth order. The proposed design procedure is completely systematic using minimum of components. The very heart of our conception is four-channel four-quadrant analog multiplier MLT04. The implementation of synthesized nonlinear resistor as a general nonlinearity in chaotic oscillator is also presented and experimentally verified

Experimental Study of the Sampled Labyrinth Chaos

In this paper, some new numerical as well as experimental results connected with the so-called labyrinth chaos are presented. This very unusual chaotic motion can be generated by mathematical model involving the scalar goniometrical functions which makes a three-dimensional autonomous dynamical system strongly nonlinear. Final circuitry implementation with analog core and digital parts can be used for modeling Brownian motion. From the viewpoint of generating chaotic motion by some electronic circuit, first step is to solve problems associated with the two-port nonlinear transfer functions synthesis. In the case of labyrinth chaos the finite dynamical range of the input variables introduced by the used active elements usually limits the performance greatly, similarly as it holds for the multi-grid spiral attractors. This paper shows an elegant way how to remove these obstacles by using uni-versal multiple-port with internal digital signal processing

Current-Controlled Current-Mode Universal Biquad Employing Multi-Output Transconductors

This paper deals with RC active biquad working in the so-called current mode (CM). The design approach uses only three transconductors (OTA) with the minimum necessary number of outputs and with only three passive grounded elements. The proposed filter has simple circuit configuration providing all standard transfer functions such as high-pass (HP), band-pass (BP), low-pass (LP), band-reject (BR) and all-pass (AP). Electronic tuning and independent adjusting of the quality factor and bandwidth of BP filter is possible. The presented circuits are verified by PSpice simulations utilizing OTAs on transistor level of abstraction. The linear parasitic effects of the real active elements in each suggested circuit are briefly discussed. Experimental verification is also given. Designed networks can be used in many applications such as antialiasing filters, in high-speed data telecommunication systems, for signal processing in the cable modems, in regulation and measurement techniques etc

Modeling Deterministic Chaos Using Electronic Circuits

This paper brings a note on systematic circuit synthesis methods for modeling the dynamical systems given by mathematical model. Both classical synthesis and integrator based method is demonstrated via the relatively complicated real physical systems with possible chaotic solution. A variety of the different active building blocks are utilized to make the final circuits as simple as possible while preserving easily measurable voltage-mode state variables. Brief experimental verification, i.e. oscilloscope screenshots, is presented. The observed attractors have some structural stability and good relationship to their numerically integrated counterparts

Communication Subsystems for Emerging Wireless Technologies

The paper describes a multi-disciplinary design of modern communication systems. The design starts with the analysis of a system in order to define requirements on its individual components. The design exploits proper models of communication channels to adapt the systems to expected transmission conditions. Input filtering of signals both in the frequency domain and in the spatial domain is ensured by a properly designed antenna. Further signal processing (amplification and further filtering) is done by electronics circuits. Finally, signal processing techniques are applied to yield information about current properties of frequency spectrum and to distribute the transmission over free subcarrier channels

Simple Chaotic Oscillator: From Mathematical Model to Practical Experiment

This paper shows the circuitry implementation and practical verification of the autonomous nonlinear oscillator. Since it is described by a single third-order differential equation, its state variables can be considered as the position, velocity and acceleration and thus have direct connection to a real physical system. Moreover, for some specific configurations of internal system parameters, it can exhibit a period doubling bifurcation leading to chaos. Two different structures of the nonlinear element were verified by a comparison of numerically integrated trajectory with the oscilloscope screenshots

Optimized Second-Order Dynamical Systems and Their RLC Circuit Models with PWL Controlled Sources

Complementary active RLC circuit models with a voltage-controlledvoltage source (VCVS) and a current-controlled current source (CCCS)for the second-order autonomous dynamical system realization areproposed. The main advantage of these equivalent circuits is the simplerelation between the state model parameters and their correspondingcircuit parameters, which leads also to simple design formulas