Nonlinear Waveform Design for Dual-Mode Radar Using Controlled Loss of Structure

Abstract

Modern radar requires waveforms that are analytically tractable for coherent processing yet irregular enough to deny exploitation by intercept receivers. This article addresses both requirements with a single nonlinear oscillator. A conservative double-well cubic–quintic oscillator is studied in a degenerate parameter regime where the reduced energy polynomial develops a double root, collapsing the generic Jacobi-elliptic orbit to an explicit closed-form solution whose nonlinear phase law sweeps the same bandwidth as a matched chirp, enabling direct performance comparison. The resulting nonflat power spectral density creates in-band nulls that suppress narrowband jammers and reduce predictability. Adding damping and periodic forcing to the same oscillator produces a period-doubling cascade into a fully chaotic low probability of intercept mode: once the oscillator is configured in its dissipative regime, the forcing amplitude $F$ alone drives the transition to chaos, with the threshold precisely identified by the largest Lyapunov exponent. The framework thus unifies a closed-form bandwidth-matched waveform and a chaos-based intercept-resistant mode within a single oscillator model.