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                <term xml:lang="en">Fluctuation phenomena</term>
                <term xml:lang="en">noise and Brownian motion</term>
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                <term xml:lang="en">Numerical simulations of chaotic systems</term>
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                <term xml:lang="en">solution of equations Low-dimensional Chaos Numerical simulations of chaotic systems Fluctuation phenomena random processes noise and Brownian motion</term>
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              <p>We develop a time-domain approach for the transition to Chaos in several periodically driven oscillators by direct integration of first-order ordinary differential equations (ODE) or functional map systems, their discrete-time counterparts. Our theoretical evaluations can be used to make detailed comparisons with experimental measurements in selected oscillating systems starting from the simple mechanical pendulum to electrical circuits: Duffing, Linsay, Testa et al. , Colpitts, then to Ikeda opto-electronic setup ... We discuss various types and origins of Chaos in these driven oscillators using bifurcation notions and tying them to some physical properties of their essential components such as Varactor Diodes in RLD (Resistance, Inductance and Diode) circuits or bistable laser excited circular cavities...</p>
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