Milan Guzan

CHUA'S SINGULARITIES: GREAT MIRACLE IN CIRCUIT THEORY

In the work [Chua, 1992], a deep intuition of its author gave rise to the choice of singularities corresponding to Chuas circuit. Therefore, it is the only one probably exhibiting three saddle points named Chuas singularities in this paper. One of the singularities is a saddle in forward time (dt > 0) of integration, whereas the other two are saddles in backward time (dt < 0) of integration. In the following, the term Chuas Chaos denotes chaos related to Chuas singularities. These singularities are the source of all special surfaces that are the subject of this contribution. We named the surface to which all other surfaces are bound as the Double-Arm Stable Manifold (DASM). The beauty and multifunctionality of this surface represents the unfathomable Intelligence in the sense of [Tolle, 2003]. The presence of the DASM in the state space is a sufficient condition for the generation of Chuas chaos or corresponding periodic windows. Since Chuas singularities are not limited by circuit morphology or the order of state equations, the research on Chuas chaos seems to be still very promising.

The control of a memory cell with the multiple stable states

The subject of this paper is control of a memory cell with the multiple stable states consisting of two resonant tunnel diodes (RTDs). One of the RTDs is an element and the other represents a load. The circuit can be described with a third-order system so that its state space is R3 and exhibits three stable states. Although we are dealing with a specific circuit and three stable states, the results presented can be generalized to the space Rn (for both n = 2 and n > 2) and multiple stable states, as well. The RTDs, however, are mentioned here only to demonstrate the all-new phenomena in R3 space.

Boundary Surface of 5-Valued Memory

The subject of research in this paper is multiple-valued (MV) memory cell—particularly the morphology of boundary surface of five-valued memory. By accepting the values of parasitic accumulation elements on the chip, very complicated morphology of the boundary surfaces occurs, which separates various attractors from each other. This is due to the occurrence of undesirable oscillations—a stable limit cycles, which makes it impossible to control memory. These dynamic attractors are so dominant that their regions of attraction even surround regions of attraction of static attractors—required logic levels of memory. Therefore, in the realization of the MV memory on the chip is necessary to know the values of the parasitic elements, because their presence may cause a malfunction of the memory. In this case, only calculation and displaying the boundary surface provides exact answers related to operation of the MV memory.

Boundary surface and stable manifold in sequential circuits

This item compares the boundary surface and stable manifold of a ternary memory. It points out to their consistency in the case of conventional saddle singularity. The other case, however, occurs at the second saddle — so called virtual. Then the boundary surface calculated using grid method differs from the stable manifold calculated by backward integration technique. The suggested procedure of calculating the stable manifold is hard for calculating and depicting a large number of trajectories — carriers of information about the stable manifold. After calculating the trajectories, stable manifold itself is depicted using the contour lines in the projection into u1, u2 plane.

Implementation of constant phase elements using low-Q band-pass and band-reject filtering sections

This paper briefly describes possibility to use band-pass and notch filters with low quality factors for straightforward synthesis of the so-called constant phase elements. These filters connected in cascade can form desired alternation of transfer function zeroes and poles. Using proposed approach one-quarter, half and three-quarter fractional-order integrator dedicated for audio and speech applications has been derived and verified by using numerical analysis. Discovered method can be generalized to arbitrary frequency range, allowed phase error and almost any biquad topology.

Dynamical Tangles in Third-Order Oscillator with Single Jump Function

This contribution brings a deep and detailed study of the dynamical behavior associated with nonlinear oscillator described by a single third-order differential equation with scalar jump nonlinearity. The relative primitive geometry of the vector field allows making an exhaustive numerical analysis of its possible solutions, visualizations of the invariant manifolds, and basins of attraction as well as proving the existence of chaotic motion by using the concept of both Shilnikov theorems. The aim of this paper is also to complete, carry out and link the previous works on simple Newtonian dynamics, and answer the question how individual types of the phenomenon evolve with time via understandable notes.

Parallelizing boundary surface computation of Chua's circuit

This paper introduces a method for performing parallel computations of the boundary surface of Chuas circuit. The presented approach could be characterized as a SIMD method which is based on the utilization of all available CPU cores. Performance comparisons between single and parallelized calculations on different computer systems are included in a table at the end of the article. The best results were observed using the highest compiler optimisation options on 64 bit architecture and using Intel i7 CPUs.

Hidden attractor and regions of attraction

This article introduced regions of attraction for new phenomenon in the field of chaotic systems: hidden attractor. Furthermore gives an answer to the question about the size of regions of attraction for stable equilibrium, hidden attractor and solutions of differential equations leading to infinity.

Current-Mode Network Structures Dedicated for Simulation of Dynamical Systems with Plane Continuum of Equilibrium

This review paper describes different lumped circuitry realizations of the chaotic dynamical systems having equilibrium degeneration into a plane object with topological dimension of the equilibriu...

Simulation of the Chua's circuit with audio output

This contribution is oriented to extend the possibilities of circuits simulation illustration that can be used in music or sensor technology. A typical example is Chuas circuit, which at bifurcation of only one parameter can generate a number of attractors. These can be showed not only in image format, but also as sound using Matlab application. It allows you to do a more complex vision of the bifurcation parameter impact in the circuit to the output signal.