In this paper we present a new version of Chen＇s system： a piecewise linear （PWL） Chert system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By...In this paper we present a new version of Chen＇s system： a piecewise linear （PWL） Chert system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By numerical simulations, we reveal chaotic behaviors and also multistability, i.e., the existence of small pararheter windows where, for some fixed bifurcation parameter and depending on initial conditions, coexistence of stable attractors and chaotic attractors is possible. Moreover, we show that by using an algorithm to switch the bifurcation parameter, the stable attractors can be numerically approximated.展开更多
The in-soil biodegradation of Stipa tenacissima(alfa)leaves was examined.Non-linear mechanical testing was performed at various biodegradation stages.Tensile strength,loading and unloading Young’s moduli and dissipat...The in-soil biodegradation of Stipa tenacissima(alfa)leaves was examined.Non-linear mechanical testing was performed at various biodegradation stages.Tensile strength,loading and unloading Young’s moduli and dissipation energy decreased with the burial time,whereas plasticity increased.Field-emission scanning electron microscopy(FE-SEM)showed that the fracture cracks propagated in the longitudinal direction in the raw material,resulting in a fracture mode consisting of a mixture of middle lamella delamination and fiber pull-out.In contrast,the cracks were perpendicular to the stem axis in the biodegraded material,demonstrating an important strength loss of the load-bearing fibers.This strength loss was correlated with rapid cellulose degradation.A novel X-ray diffraction(XRD)model was implemented in order to take into account anisotropic size broadening.For the first time,XRD demonstrated the action of biodegradation on unrefined plant tissues under quasi in-situ conditions.Biodegradation induced a progressive loss of crystalline cellulose accompanied with anisotropic crystallite thinning.展开更多
In this paper,we investigate the mathematical analysis of a mathematical model describing the virotherapy treatment of a cancer with logistic growth and the effect of viral cycle presented by a time delay.The cancer p...In this paper,we investigate the mathematical analysis of a mathematical model describing the virotherapy treatment of a cancer with logistic growth and the effect of viral cycle presented by a time delay.The cancer population size is divided into uninfected and infected compartments.Depending on time delay,we prove the positivity and boundedness and the stability of equilibria.We give conditions on which the viral cycle leads to“Jeff’s phenomenon”observed in laboratory and causes oscillations in cancer size via Hopf bifurcation theory.We establish an algorithm that determines the bifurcation elements via center manifold and normal form theories.We give conditions which lead to a supercritical or subcritical bifurcation.We end with numerical simulations illustrating our theoretical results.展开更多
基金funded by the European Regional Development Funding via RISC projectby CPER Region Haute Normandie France,the Australian Research Council via a Future Fellowship(FT110100896)Discovery Project(DP140100203)
文摘In this paper we present a new version of Chen＇s system： a piecewise linear （PWL） Chert system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By numerical simulations, we reveal chaotic behaviors and also multistability, i.e., the existence of small pararheter windows where, for some fixed bifurcation parameter and depending on initial conditions, coexistence of stable attractors and chaotic attractors is possible. Moreover, we show that by using an algorithm to switch the bifurcation parameter, the stable attractors can be numerically approximated.
文摘The in-soil biodegradation of Stipa tenacissima(alfa)leaves was examined.Non-linear mechanical testing was performed at various biodegradation stages.Tensile strength,loading and unloading Young’s moduli and dissipation energy decreased with the burial time,whereas plasticity increased.Field-emission scanning electron microscopy(FE-SEM)showed that the fracture cracks propagated in the longitudinal direction in the raw material,resulting in a fracture mode consisting of a mixture of middle lamella delamination and fiber pull-out.In contrast,the cracks were perpendicular to the stem axis in the biodegraded material,demonstrating an important strength loss of the load-bearing fibers.This strength loss was correlated with rapid cellulose degradation.A novel X-ray diffraction(XRD)model was implemented in order to take into account anisotropic size broadening.For the first time,XRD demonstrated the action of biodegradation on unrefined plant tissues under quasi in-situ conditions.Biodegradation induced a progressive loss of crystalline cellulose accompanied with anisotropic crystallite thinning.
文摘In this paper,we investigate the mathematical analysis of a mathematical model describing the virotherapy treatment of a cancer with logistic growth and the effect of viral cycle presented by a time delay.The cancer population size is divided into uninfected and infected compartments.Depending on time delay,we prove the positivity and boundedness and the stability of equilibria.We give conditions on which the viral cycle leads to“Jeff’s phenomenon”observed in laboratory and causes oscillations in cancer size via Hopf bifurcation theory.We establish an algorithm that determines the bifurcation elements via center manifold and normal form theories.We give conditions which lead to a supercritical or subcritical bifurcation.We end with numerical simulations illustrating our theoretical results.
