Estimating and enlarging the region of attraction of multi-equilibrium points system by state-dependent edge impulses

The main objective of this paper is to propose an optimal finite duration treatment method for cancer. A mathematical model is proposed to show the interactions between healthy and cancerous cells in the human body. To extend the existing models, the effect of vaccine therapy and chemotherapy are also added to the model. The equilibrium points and the related local stability are derived and discussed. It is shown that the dynamics of the cancer model must be changed and modified for finite treatment duration. Therefore, the vaccine therapy is used to change the parameters of the system and the chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. For optimal chemotherapy, an optimal control is used based on state dependent Riccati equation (SDRE). It is shown that, in spite of eliminating the treatment, the system approaches the healthy state conditions. The results show that the development of optimal vaccine-chemotherapy protocols for removing tumor cells would be an appropriate strategy in cancer treatment. Also, the present study states that a proper treatment method not only reduces the population of the cancer cells but also changes the dynamics of the cancer.

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Host-pathogen interaction for larvae oysters with salinity dependent transmission

Advances in Difference Equations ◽

10.1186/s13662-019-2339-2 ◽

2019 ◽

Vol 2019 (1) ◽

Author(s):

Kalanyu Sunthawanic ◽

Kornkanok Bunwong ◽

Wichuta Sae-jie

Keyword(s):

Equilibrium Points ◽

Upper And Lower Bounds ◽

Region Of Attraction ◽

Free Swimming ◽

Free Living ◽

Sis Model ◽

Oyster Population ◽

Host Pathogen Interaction ◽

Host Pathogen ◽

Homogeneous Environment

Abstract Mathematical models of host-pathogen interactions are proposed and analyzed. Here hosts are oyster population in a free-swimming larval stage and assumably live in the closed homogeneous environment. In terms of an epidemic, they are classified into two states, namely susceptible and infectious hosts. The epidemic model of oyster hosts with seasonal forced transmission is firstly described by the SIS model where the region of attraction, the existence of equilibrium points, their stability conditions, and upper and lower bounds on the attack rate are investigated. Then free-living pathogen is introduced in the oyster area. Numerical simulations are finally carried out by making use of the various salinity-dependent transmissions in support of the hypothesis that the lower the salinity level, the lower oyster’s immunity.

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Flux-Charge Analysis of Initial State-Dependent Dynamical Behaviors of a Memristor Emulator-Based Chua’s Circuit

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127418501201 ◽

2018 ◽

Vol 28 (10) ◽

pp. 1850120 ◽

Cited By ~ 18

Author(s):

Mo Chen ◽

Bocheng Bao ◽

Tao Jiang ◽

Han Bao ◽

Quan Xu ◽

...

Keyword(s):

Equilibrium Points ◽

Chua’S Circuit ◽

Initial State ◽

Chua's Circuit ◽

Dynamical Behaviors ◽

State Dependent ◽

Initial States ◽

Original Line ◽

Flux Charge ◽

Memristor Emulator

It is known that dynamical behaviors of memristive circuit are significantly affected by its initial states, which are difficult to be explicitly analyzed or controlled in voltage–current domain and have become great obstacles for its potential engineering applications. In this paper, the complex initial state-dependent dynamical behaviors of a physically realized memristive Chua’s circuit are detailed and investigated using incremental flux-charge modeling method. This circuit is modeled in terms of incremental flux and charge, in which the original line equilibrium point is converted into some determined equilibrium points relying on the initial states of the dynamic elements. Moreover, the special initial state-dependent behaviors are transformed into system parameter-associated behaviors. Consequently, the detailed influences of each initial state, even the occurrence of hidden oscillations, can readily be theoretically interpreted. Finally, the initial state-dependent behaviors are physically captured and directed in the equivalent realization circuit of the incremental flux-charge model.

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