Arnold tongues of divergence in the Caputo fractional standard map of nilpotent matrices

Arnold tongues of divergence in the Caputo fractional standard map of nilpotent matrices are explored in this paper. The scalar iterative variables in the Caputo fractional standard map are replaced by iterative matrix variables. The divergence effects induced by the nilpotent matrices result in specific patterns of Arnold tongues. Automatic machine classification techniques help to identify different types of Arnold tongues according to the dynamics of the transient processes of the system. Computational experiments are used to validate theoretical insights and to reveal the patterns of Arnold tongues of divergence.