Abstract
We describe an extremely simple second order analogue electrical circuit for simulating the two-well Duffing-Holmes mathematical oscillator. Numerical results and analogue electrical simulations are illustrated with the snapshots of chaotic waveforms, with the phase portraits (the Lissajous figures) and with the stroboscopic maps (the Poincar´e sections).
Highlights
Electrical circuits generating complex and chaotic waveforms are convenient tools for imitating temporal evolution of nonlinear dynamical systems and for simulating differential equations
We describe an extremely simple analogue electrical circuit dedicated for simulation the Duffing-Holmes (DH) equation [11,12,13,14]
We have designed and investigated an electrical circuit, which can be treated as an electrical analogue of the Duffing-Holmes mathematical oscillator
Summary
Electrical circuits generating complex and chaotic waveforms are convenient tools for imitating temporal evolution of nonlinear dynamical systems and for simulating differential equations. The third approach is based on building some specific analogue electrical circuit for a given differential equation. Despite its limitation to a specific equation, the ”intrinsic” electrical circuits have an attractive advantage due to their simplicity and cheapness. Such circuits comprise only small number of discrete electrical components: resistors, capacitors, inductors, semiconductor diodes, may include a single (sometimes several) operational amplifier. Differences between the ”intrinsic” analogue electrical circuits, simulating behaviour of dynamical systems, and the conventional analogue computers are discussed and emphasised in [20]
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