Computing with nonlinear dynamical systems

We discuss the computational capabilities of nonlinear coupled oscillatory networks. Oscillator neural networks (ONNs) consist of fully to sparsely coupled oscillator systems that exhibit rich dynamical states. Though, how to ensure that the ONN dynamics can effectively perform computation and under which conditions, is the focus of our research.
ONN computational model is based on oscillators acting as an activating neuron and coupling strengths between oscillators serve as the synaptic connections, taking inspiration from biological neural networks. We show that information can be encoded in the phase relations of oscillators that can further be exploited either for in-memory computing or solving combinatorial optimization problems.
Both oscillator behavior and coupling strengths between oscillators play an important role in the dynamics of the system by enabling oscillators to reach in-phase, out-of-phase or chaotic synchronization states. We investigate both linear and nonlinear oscillators to understand the difference in the complex dynamics that ONNs can achieve and their impact on computational tasks.
We present a detailed study of exploiting the behavior of nonlinear oscillators for performing different computational tasks. We study fully connected coupled oscillatory networks with nonlinear oscillator such as van der Pol model. Our results show that certain computational tasks such as pattern retrieval or solving optimization problems benefit from harnessing nonlinearity of oscillators that allows for higher accuracy and fast time to solution.