A family of multimodal dynamic maps

► A family of chaotic multimodal logistic maps is proposed and basins of attraction of each fixed point of the family are constructed in terms of the bifurcation parameter. ► The attractor domain in the parameter space increases as a number of modals grows up. ► Each multimodal logistic map displays a stretching-and-folding structure and its bifurcation diagrams reproduce scaled bifurcations of the classical logistic map. We introduce a family of multimodal logistic maps with a single parameter. The maps domain is partitioned in subdomains according to the maximal number of modals to be generated and each subdomain contains one logistic map. The number of members of a family is equal to the maximal number of modals. Bifurcation diagrams and basins of attraction of fixed points are constructed for the family of chaotic logistic maps.