Analysis of chaotic behavior in lumped-distributed circuits applied to the time-delayed Chua's circuit

Abstract-The purpose of this brief is that, by an application of the method of characteristics, we analyze chaotic phenomena in Chua's circuit with lossy transmission line. The transmission line is replaced by the equivalent lumped circuit and a time-delayed element so that it can be solved efficiently by the Runge-Kutta method. It is found from numerical experiments that the circuit has complicated and interesting chaotic attractors.

Section: Introductionmentioning

confidence: 99%

Analysis of Chua's circuit with transmission line

Kawata

Nishio

Ushida

1997

“…Applying the transformation z = e sT our stability study can be translated to the s plane as in [11]. Figure 2 shows excellent agreement between the analytical and the numerical method for a second to fourthorder Gear discretization.…”

Section: A Equilibrium Pointsmentioning

confidence: 88%

“…If we apply the idea contained in (11) to each of the products that appear in (2), we obtain an equivalent formulation in the form…”

Section: Resulting System Of Equationsmentioning

confidence: 99%

See 1 more Smart Citation

A discrete-time approach to the steady-state and stability analysis of distributed nonlinear autonomous circuits

Bonet-Dalmau

Pala-Schonwalder

2000

Abstract-We present a direct method for the steady-state and stability analysis of autonomous circuits with transmission lines and generic nonlinear elements. With the discretization of the equations that describe the circuit in the time domain, we obtain a nonlinear algebraic formulation where the unknowns to determine are the samples of the variables directly in the steady state, along with the oscillation period, the main unknown in autonomous circuits. An efficient scheme to build the Jacobian matrix with exact partial derivatives with respect to the oscillation period and with respect to the samples of the unknowns is described. Without any modification in the analysis method, the stability of the solution can be computed a posteriori constructing an implicit map, where the last sample is viewed as a function of the previous samples. The application of this technique to the time-delayed Chua's circuit (TDCC) allows us to investigate the stability of the periodic solutions and to locate the period-doubling bifurcations.

“…The presence of leads to a nonlinear differentialdifference equation [1], [10], which does not admit a complete analytical treatment (see [11]). So far, some partial results on the qualitative behavior of the circuit have been reported in [10] and [12].…”

mentioning

confidence: 99%

Qualitative analysis of the dynamics of the time-delayed Chua's circuit

Biey

Bonani

Gilli

et al. 1997

Abstract-Several variants of the Chua's circuit have been recently proposed in order to enlarge the class of nonlinear phenomena that can be generated by relatively simple circuits. In particular, Sharkovsky et al. proposed the so called timedelayed Chua's circuit (TDCC), where the original lumped LC resonator is substituted by an ideal transmission line, thereby generating an infinite dimensional system. The TDCC has been studied in details in the absence of the capacitor C; the only lumped dynamic element left in the circuit. This paper studies the effects of the presence of C on the dynamics of the circuit. After recasting the circuit equations in a suitable normalized form, their characteristic equation is theoretically investigated and the regions in the parameter space where all the eigenvalues have negative real part are exactly evaluated along with all the possible qualitative eigenvalue distributions. This analysis allows for a qualitative description of the TDCC dynamics in presence of the capacitor C: In particular, it is shown that, for particular sets of circuit parameters, an even small value of C; e.g., a parasitic element, may completely change the behavior of TDCC and that, on the other hand, any TDCC, exhibiting the periodadding phenomenon for C = 0; still continues to present this phenomenon even if a small capacitor C is added to the circuit.