Simulation of nonlinear dynamical systems in CUDAynamics interactive suite

The analysis of complex nonlinear dynamical systems, particularly memristive models relevant to neuromorphic engineering, is hindered by the computational bottleneck of traditional simulation tools and their disconnect from interactive exploration. This work introduces CUDAynamics, a new interactive software suite that overcomes this limitation through the tight integration of parallel, GPU-accelerated simulation with an immediate mode graphical interface. The suite enables dynamic control of parameters and numerical solvers with simultaneous visualization of system’s time-domain, phase- and parameter-space diagrams, facilitating rapid hypothesis testing and the discovery of complex behaviors such as multistability, persistent and transient chaos. We demonstrate its capabilities through an analysis of a memristive Josephson junction model, performing extensive parameter sweeps and bifurcation analysis to map regions of diverse dynamics: coexisting limit cycles with basins of attraction of different complexity, nested and external chaotic attractors alongside a periodic orbit, intermittent and transient chaotic modes. The numerical results are validated through cross-comparison with SPICE-based simulation in Multisim and, critically, through measurements from a physically constructed analog circuit prototype. The close agreement across all three platforms confirms the predictive accuracy of the simulation framework. Benchmarking studies against established CUDA-based implementations confirmed a significant performance advantage of the CUDAynamics suite.