Course Content (Syllabus)
Nonlinear Circuit Elements. The nonlinear resistor (series and parallel connections, concave and convex resistors, dc operating points, small signal analysis). Nonlinear capacitors and inductors.
Operational-amplifier circuits. Device description, characteristics and model. OP-AMP circuits operating in the linear region. OP-AMP circuits operating in the nonlinear region.
First-order circuits. Circuits driven by dc sources, circuits driven by piecewise-constant signals, the dynamic route, jump phenomenon and relaxation oscillation). Second-order circuits. Tunnel diode and Josephson junction circuits, equilibrium states and operating points.
Nonlinear oscillation. Basic negative-resistance oscillator, physical mechanisms for oscillation, phase portrait of typical oscillators. Van der Pol oscillator, Duffing oscillator, Duffing-Ueda oscillator.
Introduction to nonlinear dynamics. Poincaré maps, bifurcation diagrams, Lyapunov exponents.
From periodicity to chaos. Routes to chaos (period-doubling, collapse of tori, intermittency). Antimonotonicity. Crises of chaotic attractors.
Chaotic dynamics of the R-L-varactor diode circuit.
Chaotic dynamics of Chua’s circuit family.
Memristors (from periodicity to chaos)
Nonlinear circuits, Chaos, Antimonotonicity, bifurcation diagram, phase portrait, Poincare, Memristor,