Analysis of leukaemic cells dynamics with multi‐stage maturation process using a new non‐linear positive model with distributed time‐delay

Replication of period-doubling route to chaos in impulsive systems

“…Using the technique presented in this paper it is possible to obtain high dimensional systems with delay which possess chaotic motions. The obtained theoretical results may be applied to various fields such as neural networks, secure communication, robotics, medicine, biology, economics, and lasers in which dynamics are described through differential equations with delay [5,6,7,8,11,12].…”

On the Admissibility and Stability of Multiagent Nonlinear Interconnected Positive Systems With Heterogeneous Delays

“…Via an integral action, the delay operator has accumulative effect over the past values of the dynamics. For this reason, distributed delay systems exist in a wide range of applications [2]. Thus, if the interconnected system is modelled including heterogeneous communication delays ( n ∈ N constant delays and m ∈ N distributed delays) as follow: (7) where…”

“…Let consider cells dynamics with multi-stage maturation process [2], the process dynamics are given by the following distributed delay system:…”

“…We invite the reader to refer [2] to get a detailed presentation of the biological system model in (71). The parameters and functions of this model are given in [24]- [27]).…”

“…Then, we exploit the time function and its time derivative to develop the global asymptotic stability and instability conditions for the multi-agent nonlinear positive interconnected systems with constant and distributed delays. We illustrate the results of the proposed method on a biological problem proposed recently in [2] and which describes stem cells dynamics in hematopoiesis with multi-stage of maturation.…”