Cyclical thrombocytopenia (CT) is a rare hematological disease characterized by periodic oscillations in circulating platelet counts. In almost all CT patients, other cell lines show no sign of oscillation, but recently a CT patient was reported with significant oscillations in circulating neutrophils (in the same period as the platelets). In this paper, we attempt to understand this phenomenon through a previously published model of human hematopoiesis. We have investigated a variety of possible oscillation patterns that may appear when alterations occur in the control parameters in the platelet regulatory dynamics. Our results indicate that the platelet maturation time and the differentiation rate from hematopoietic stem cells (HSCs) into the platelet cell line play important roles in the emergence of various types of CT like oscillations. Moreover, we find different oscillation patterns, including CT and cyclical neutropenia like oscillations, with certain parameter values in the platelet compartment. A bifurcation analysis revealed the different origins of these oscillation patterns. We also identified bistable dynamics which indicate the potential importance of system history in the treatment of these diseases. Together, these results demonstrate the possible origins for various oscillation patterns dependent on alterations in the platelet cell line control mechanisms. One of the important origins may be related to the regulation of apoptosis in platelet precursors. Crown Copyright © 2018. Published by Elsevier Ltd. All rights reserved.