Dynamics and the periodic solutions of the delayed non-smooth Internet TCP-RED congestion control system via HB–AFT

作者：

Highlights：

• For the first time, approximate expressions of periodic solutions of delayed non-smooth dynamical system are obtained.

• Approximate expressions of non-impacting and impacting periodic solutions of delayed non-smooth system are obtained.

• For the first time, prediction of periodic oscillations of delayed non- smooth TCP-RED system are executed successfully.

• Three kinds of bi-stability have been found.

• An impacting periodic solution traversing both thresholds has been also obtained.

• A route to chaos, i.e., intermittent to chaos, has been also found.

• Some solutions seem like periodic solutions are found to be complex oscillations with high frequency and small amplitude.

摘要

•For the first time, approximate expressions of periodic solutions of delayed non-smooth dynamical system are obtained.•Approximate expressions of non-impacting and impacting periodic solutions of delayed non-smooth system are obtained.•For the first time, prediction of periodic oscillations of delayed non- smooth TCP-RED system are executed successfully.•Three kinds of bi-stability have been found.•An impacting periodic solution traversing both thresholds has been also obtained.•A route to chaos, i.e., intermittent to chaos, has been also found.•Some solutions seem like periodic solutions are found to be complex oscillations with high frequency and small amplitude.

论文关键词：Delayed non-smooth,HB-AFT,TCP-RED congestion control system,Periodic solutions,Chaos

论文评审过程：Received 18 March 2019, Revised 4 June 2019, Accepted 10 June 2019, Available online 25 June 2019, Version of Record 25 June 2019.

论文官网地址：https://doi.org/10.1016/j.amc.2019.06.032