HOPF BIFURCATION OF AN OSCILLATOR WITH QUADRATIC AND CUBIC NONLINEARITIES AND WITH DELAYED VELOCITY FEEDBACK

This paper studies the local dynamics of an SDOF system with quadratic and cubic stiffness terms,and with linear delayed velocity feedback.The analysis indicates that for a sufficiently large velocity feedback gain,the equilibrium of the system may undergo a number of stability switches with an increase of time delay,and then becomes unstable forever.At each critical value of time delay for which the system changes its stability,a generic Hopf bifurcation occurs and a periodic motion emerges in a one-sided neighbourhood of the critical time delay.The method of Fredholm alternative is applied to determine the bifurcating periodic motions and their stability.It stresses on the effect of the system parameters on the stable regions and the amplitudes of the bifurcating periodic solutions.

Noise-induced bistable switching dynamics through a potential energy landscape

Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation between two species as another positive feedback is added to a generic interlinked positive-feedback-loop model originating from many realistic biological circuits.A stochastic fluctuation of the positive feedback strength is introduced in a bistable interval of the feedback strength,and bistability appears for the moderate feedback strength at a certain noise level.Stability analysis based on the potential energy landscape is further utilized to explore the noise-induced switching behavior of two stable steady states.

Time-delay effects on the dynamics of Linard type equation with fast and slow variables

Time-delay effects on the dynamics of Li^nard type equation with one fast variable and one slow variable are investigated in the present paper. By using the methods of stability switch and geometric singular perturbation, time-delay-induced complex oscillations and bursting are investigated, and in several case studies, the mechanism of the generation of the complex oscillations and bursting is illuminated. Numerical results demonstrate the validity of the theoretical results.

Highly reliable bipolar resistive switching in sol-gel derived lanthanum-doped PbTiO_3 thin film: Coupling with ferroelectricity?

Nanoscale PbxLa1-,Ti1-x/4O3 （PLT） thin film has been fabricated on Pt／Ti／SiO2／Si substrates by chemical solution deposition （CSD） method. Ferroelectricity of the fresh-made PLT thin film has been clearly detected through piezoelectric force microscopy （PFM） by writing reversible ferroelectric domains. However, PLT thin film also shows off-standard ferroelectric hysteresis loops highly dependent on frequency, indicating large amount of mobile space charges in the film. Subsequent current-voltage （C-V） studies show that sandwich-like Pt／PLT／Pt structure exhibits notable bipolar resistive switching （BRS） characteristics with high stability （〉 103 switching cycles）. It is found that the C-V curves of both high- and low-resistance states have the feature of space-charge-limited current （SCLC） conduction, indicating important roles of defects in the conduction. X-ray photoelectron spectroscopy measurement further verifies that oxygen vacancies based conductive filament mechanism is likely responsible for the observed RS effect. Our demonstration of stable RS effect in the PLT thin film and its possible coupling with ferroelectricity is promising in device development and applications, such as development of ferroelectric-tunable RS memories.

Bifurcation Analysis of the Regulatory Modules of the Mammalian <i>M/G₁</i>Phase with Time Delay

G0/G1 “gaps” joint the S phase and M phase to form the cell cycle. The dynamics of enzyme reaction to drive the target protein production in M phase is analyzed mathematically. Time delay is introduced since the signal transmission need time in G0/G1 “gaps” phase. Hopf bifurcation of DDEs model is analyzed by applying geometrical analytical method. The instability oscillating periodic solutions arise as subcritical Hopf bifurcation occurs. The Hysteresis phenomena of the limit cycle are also observed underlying the saddle-node bifurcation of the limit cycle. Due to stability switching, interestingly, the bifurcating periodical solution dies out near the vicinity of Hopf lines. By Lyapunov-Schmidt reduction scheme, the normal form is computed on the center manifold. Finally, it is verified that the theory analytical results are in coincidence with the numerical simulation.

Impact of time delay and cooperation strategy on the stability of a predator-prey model with Holling type III functional response

In this paper,we propose and analyze a delayed predator-prey model with Holling type III functional response taking into account cooperation behavior in predators.The time delay is introduced in the attack rate to represent the time necessary to trigger the attack.Each analytical result is followed by an ecological interpretation.We investigate the effect of hunting cooperation on both the number and the level of positive steady states.We observe that the level of the positive equilibrium decreases when increasing the hunting cooperation parameter.Then,we study the impact of the delay as well as the cooperation in hunting on the dynamics of the system.We prove that the presence of delay in the attack rate induces stability switches around the coexisting equilibrium when predators cooperate.In addition,we consider the discrete delay as a bifurcation parameter and prove that the model undergoes a Hopf-bifurcation at the coexisting equilibrium when the delay crosses some critical values.Numerical simulations are presented to confirm our analytical findings.

Decyloxyphenyl-substituted Quinoxaline-embedded Conjugated Electrochromic Polymers with High Switching Stability and Fast Response Speed

Two novel decyloxyphenylquinoxaline-based donor-acceptor （D-A） electroactive monomers bearing dialkoxythiophene as the donor unit are synthesized using Stille coupling reaction. The corresponding polymers, poly[2,3- bis（4-decyloxyphenyl）-5,8-bis（3,4-dimethoxylthiophen-2-yl）quinoxaline] （P1） and poly[2,3-bis（4-decyloxyphenyl）-5,8- bis（2,3-dihydrothieno[3,4-b][1,4]dioxin-5-yl）quinoxaline] （P2）, are directly deposited onto the working electrode surface by electropolymerization. All materials were characterized by nuclear magnetic resonance （NMR）, mass spectrometry （MS）, scanning electron microscopy （SEM）, cyclic voltammetry （CV）, ultraviolet-visible absorption spectrometry （UV-Vis） and spectro-electrochemical measurements. Electrochemical studies demonstrate that both polymers are capable of showing both reasonable n- and p-doping processes, and advanced long-term switching stabilities. 3,4-Ethylenedioxythiophene substituted for 3,4-dimethoxythiophene as a donor unit, which enhances the conjugated double-bond character of the conducting polymer, thus leading to a lower electronic band-gap. Likewise, the neutral state color of the synthesized polymer tuned from blue to blue-green corresponding to the red shift of the maximum absorption wavelengths in the visible region. In addition, kinetics study of P1 revealed 42% （595 nm）, 30% （839 nm） and 69% （1500 nm） transmittance changes （A7%）, while P2 exhibited 32% （740 nm）, 71% （2000 nm） at the dominant wavelengths. It was also observed that both films could switch quickly between the neutral state and oxidation state, with the response time less than 1 s both in visible and near infrared regions.

Stability and bifurcation analysis for a delayed viral infection model with full logistic proliferation

In this paper,we study a delayed viral infection model with cellular infection and full logistic proliferations for both healthy and infected cells.The global asymptotic stabil-ities of the equilibria are studied by constructing Lyapunov functionals.Moreover,we investigated the existence of Hopf bifurcation at the infected equilibrium by regarding the possible combination of the two delays as bifurcation pararmeters.The results show that time delays may destabilize the infected equilibrium and lead to Hopf bifurcation.Finally,numerical simulations are carried out to illustrate the main results and explore the dynamics including Hopf bifurcation and stability switches.

Robust observer-driven switching stabilization of switched linear systems

In this work, we study the robust observer-driven switching stabilization problem of switched linear sys- tems. Under the condition that each subsystem is completely observable, with the observer-driven switching law which makes the system exponentially stable for the nominal system, we prove that the overall system is robust against structural/switching perturbations and is input/output to state stable for unstructural perturbations.

A STAGE-STRUCTURED AND HARVESTING PREDATOR-PREY SYSTEM

A predator-prey system with independent harvesting in either species and BeddingtonDeAngelis functional response is investigated. By analyzing characteristic equations and using an iterative technique,we obtain a set of easily verifiable sufficient conditions,which ensure the local and global stability of the nonnegative equilibria of the system. It is also shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities. Numerical simulations are carried out to illustrate the validity of our results.