  We investigate the bound on the Lyapunov exponents by a charged particle in
Kerr-Newman-de Sitter black holes using analytic and numerical methods. We
determine whether the Lyapunov exponent can exceed the bound by an electrically
charged particle with an angular momentum. Our tests are applied to the de
Sitter spacetime by the positive cosmological constant such as
Reissner-Nordstr\"{o}m-de Sitter, Kerr-de Sitter, and Kerr-Newman-de Sitter
black holes. In particular, we consider Nariai and ultracold limits on these
black holes for our tests. From our analysis results, there remain violations
on the bound under the positive cosmological constant, and electric charge and
angular momentum of the particle significantly impact the Lyapunov exponent.
