ICO Learning assisted characterization of Transient Chaos in PT-symmetric Liénard system

In this article, we investigate the implications of the unsupervised learning technique known as Input-Correlations (ICO) learning in the temporal dynamics of two linearly coupled PT-symmetric Liénard oscillators. We find that on increasing the amplitude of the external periodic drive, the system exhibits period-doubling cascade to chaos. In the period-4 regime, we observe the emergence of transient chaos which has been further validated by the maximal Finite-Time Lyapunov Exponent (FTLE) and the Hilbert Transform. In the transiently chaotic regime, we deploy ICO learning from which we identify that when there is emergence of transiently chaotic dynamics, the synaptic weight associated with the loss oscillator exhibits stationary temporal evolution. This signifies that in the periodic regime, there is no overlap between the filtered signals obtained from the time-series of the coupled PT-symmetric oscillators. In addition, the temporal evolution of the weight associated with the stimulus mimics the behaviour of the Hilbert transform of the time-series.