This paper strives to achieve a comprehensive review of chaos in analog circuits and lumped electronic networks. Readers will be guided from the beginning of the investigations of simple electronic circuits to the current trends in the research into chaos. The author tries to provide the key references related to this issue, including papers describing modern numerical algorithms capable of localizing chaotic and hyperchaotic motion in complex mathematical models, interesting full on-chip implementations of chaotic systems, possible practical applications of entropic signals, fractional-order chaotic systems and chaotic oscillators with mem-elements.

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 equilibrium structure equals one. This property has limited amount (but still increasing, especially recently) of third-order autonomous deterministic dynamical systems. Mathematical models are generalized into classes to design analog networks as universal as possible, capable of modeling the rich scale of associated dynamics including the so-called chaos. Reference state trajectories for the chaotic attractors are generated via numerical analysis. Since used active devices can be precisely approximated by using third-level frequency dependent model, it is believed that computer simulations are close enough to capture real behavior. These simulations are included to demonstrate the existence of chaotic motion.

This paper presents a new concept of a capacitance multiplier using the topology of differential voltage buffer and current conveyor, where the capacitor is connected to the current input terminal. The presented topology overcomes the typical issue known from similar solutions, i.e. creation of an undesired lossy character of the impedance plot. The added feedback path in the structure serves for minimization of the serial parasitic resistance of the current input terminal as well as the output resistance of differential voltage buffer. The electronic driving of the current and voltage internal gains of the active elements allows the adjustment of the capacitance multiplication factor as well as readjustment of the overall capacitance structure between the lossy and lossless modes of operation. The adjustment of the multiplication factor intentionally targets low ranges of gains. Despite that the multiplication factor equals or is less than 1, the range of adjustability is very wide. Simple modifications of the proposed concept leading to the differential-mode operation and enhancement of the multiplication factor are shown and explored. They were experimentally tested in more than 2 decades, from 0.03 to 5.8 nF, and controlled by single DC voltage from 0.1 to 1.0 V. The outputs of experimental measurements meet with the PSpice simulations and confirm the design validity.

This paper presents a new autonomous deterministic dynamical system with equilibrium degenerated into a plane-oriented hyperbolic geometrical structure. It is demonstrated via numerical analysis and laboratory experiments that the discovered system has both a structurally stable strange attractor and experimentally measurable chaotic behavior. It is shown that the evolution of complex dynamics can be associated with a single parameter of a mathematical model and, due to one-to-one correspondence, to a single circuit parameter. Two-dimensional high resolution plots of the largest Lyapunov exponent and basins of attraction expressed in terms of final state energy are calculated and put into the context of the discovered third-order mathematical model and real chaotic oscillator. Both voltage- and current-mode analog chaotic oscillators are presented and verified by visualization of the typical chaotic attractor in a different fashion.