Abstract
This paper presents and briefly discusses recent observations of dynamics associated with isolated generalized bipolar transistor cells. A mathematical model of this simple system is considered on the highest level of abstraction such that it comprises many different network topologies. The key property of the analyzed structure is its bias point since the transistor is modeled via two-port admittance parameters. A necessary but not sufficient condition for the evolution of autonomous complex behavior is the nonlinear bilateral nature of the transistor with arbitrary reason that causes this effect. It is proved both by numerical analysis and experimental measurement that chaotic motion is miscellaneous, robust, and it is neither numerical artifact nor long transient motion.
Highlights
Chaos can be considered as long-time unpredictable behavior of a dynamical system that is both nonlinear and, in the autonomous case, has at least three degrees of freedom
Chaotic systems are very sensitive to the changes of initial conditions; this sensitivity is caused by exponential divergency of neighborhood orbits but, at the same time, the generated strange attractor is bounded into finite state space volume
Conditions leading to chaotic motion can be summarized as follows: 1. General mathematical models analyzed in this paper (3) and (10) contain normalized values of all accumulation elements
Summary
Chaos can be considered as long-time unpredictable behavior of a dynamical system that is both nonlinear and, in the autonomous case, has at least three degrees of freedom. Chaotic systems are very sensitive to the changes of initial conditions; this sensitivity is caused by exponential divergency of neighborhood orbits but, at the same time, the generated strange attractor is bounded into finite state space volume. The boundedness of the strange attractor is due to the suitable nonlinearity of the vector field. Recent studies reveal that fixed points are not crucial for the evolution of chaos. There are several mathematical models with equilibrium degenerated into higherdimensional geometric structures or chaotic systems without equilibrium. A wide variety of chaotic dynamical systems that exhibit the so-called hidden attractors are available via internet search
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