Double Time Delays Research Articles

Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps

In this paper, a hybrid stochastic prey–predator system with double time delays and commercial exploitation is established, where combined dynamic effects of telephone noise and Lévy jumps on stochastic population dynamics are taken into accounts. Existence and uniqueness of globally positive solution to the proposed system are investigated. By constructing appropriate stochastic Lyapunov functions, existence of an ergodic and unique stationary distribution of the positive solution is discussed. Sufficient conditions for permanence in mean and extinction of corresponding population are derived. Furthermore, sufficient and necessary criteria for optimal exploitation strategy are studied. Numerical simulations are carried out to show consistency with theoretical analysis.

Abstract 4717: Effective preclinical management of angiosarcoma with oral paclitaxel

Abstract Angiosarcomas are characterized by proliferating anaplastic cells derived from blood vessels. While there is a lack of approved treatments for angiosarcomas, weekly intravenous (IV) paclitaxel has shown some benefit. However, IV paclitaxel therapy is commonly accompanied with hypersensitivity reactions and irreversible neuropathy. Oral paclitaxel (“Oraxol”; paclitaxel co-administered with HM30181A, a non-absorbable P-gp inhibitor) eliminates the risk of hypersensitivity to IV formulations while reducing neuropathy with the potential for improved efficacy. Oral paclitaxel is currently being tested in a pivotal phase III trial for metastatic breast cancer in addition to multiple phase I/II trials for solid tumors. Here, we aim to expand the therapeutic application of oral paclitaxel to the treatment of angiosarcomas. An MTT assay was utilized to determine the potency of paclitaxel against mouse angiosarcoma cell lines (MS1, SVRA221a, and SVRbag4) and a human endothelium cell line (HMEC-1). The potency (IC50) of paclitaxel was estimated to be 1.8 ± 0.36 ng/mL for MS1, 1.8 ± 1.0 ng/mL for SVRA221a, 3.9 ± 1.0 ng/mL for SVRbag4, and 0.46 ± 0.23 ng/mL for HMEC-1 cells. Immunofluorescence was used to examine the effect of paclitaxel on microtubule polymerization in the angiosarcoma cell lines. Paclitaxel induced polymerization of microtubules accompanied with condensed and rounded morphology starting at 4.2 - 8.5 ng/mL. To assess the efficacy of oral paclitaxel, MS1, SVRA221a, and SVRbag4 xenograft models were developed. The MS1 tumors grew too slowly while the SVRbag4 tumors did not reach tumor size endpoint due to necrosis and ulceration, so tumor doubling time and tumor growth delay could not be determined. In the SVRA221a angiosarcoma xenograft model, oral paclitaxel administered for three consecutive days, weekly for three weeks, resulted in dose-dependent tumor growth inhibition and subsequent increased survival. Mice treated with 20 mg/kg HM30181A and 30 mg/kg paclitaxel experienced the greatest tumor growth inhibition with 57.5% survival on Day 15, whereas 20 mg/kg and 40 mg/kg paclitaxel administered with 20 mg/kg HM30181A demonstrated 32.3% and 51.6% survival on Day 15 of treatment, respectively. The antitumor effect and increased survival appeared to plateau between 30 and 40 mg/kg, suggesting that increasing the dose above 30 mg/kg provides no additional benefit. Cavernous blood-filled neoplastic vessels were consistently formed in vehicle and 10 mg/kg paclitaxel-treated groups. However, few to none were present in 20, 30, or 40 mg/kg paclitaxel-treated groups, suggesting oral paclitaxel demonstrated dose-dependent efficacy in this angiosarcoma murine model. Oral paclitaxel has been granted Orphan Drug Designation by the US FDA for the treatment of angiosarcomas and a pilot study of oral paclitaxel in patients with cutaneous angiosarcoma is planned (NCT03544567). Citation Format: Murray J. Cutler, Krista E. Belko, Yahao Bu, Alissa R. Verone-Boyle, David Cutler, Wing-Kai Chan, Rudolf Kwan, Johnson Y. Lau, Michael P. Smolinski. Effective preclinical management of angiosarcoma with oral paclitaxel [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 4717.

Bifurcations and Dynamics of a Predator–Prey Model with Double Allee Effects and Time Delays

In this paper, a predator–prey system with double Allee effects and time delay is considered. On the one hand, by using time delay as bifurcation parameter, the stability of the interior equilibrium point is studied. It is shown that under certain assumptions the equilibrium point of the delay model is locally asymptotically stable for all delay values, otherwise, there is a critical value, such that the equilibrium point is locally stable when time delay is less than the critical value, and Hopf bifurcation occurs when the delay crosses the critical value. Numerical simulations are carried out to validate the analytical results. On the other hand, we investigate the following four submodels respectively: the time-delayed system without Allee effect, the time-delayed system with Allee effect on predator, the time-delayed system with Allee effect on prey and the time-delayed system with double Allee effects. Compared with the situation without Allee effects, Allee effect on predator causes a decline of the equilibrium state of the predator, the equilibrium state of the prey and critical time delay are almost unaltered; Allee effect on prey and Allee effect on prey and predator all lead to the descent of the equilibrium state of the predator and prey, inversely, and critical time delay has an obvious rise. A comparison of the four cases indicates that Allee effect can alter the magnitudes of predator density and prey density at future time, the time that predator and prey cost to keeping steady state is also changed.

Wnt2 knock down by RNAi inhibits the proliferation of in vitro-cultured human keloid fibroblasts.

To study the effect of knocking down wingless-related MMTV integration site 2 (Wnt2) expression by RNAi on the growth and signaling pathways of ex vitro-cultured keloid fibroblasts (KFB).Human KFB were isolated from 10 keloid patient specimens. The KFB cells were then transfected with 4 pairs of small interfering RNA (siRNA) targeting human Wnt2, respectively. Reverse transcriptase-polymerase chain reaction and Western blot analysis were conducted to verify the knock down of Wnt2, and the expression of β-catenin glycogen synthase kinase-3β (GSK-3β) and cyclin D1 were examined.siRNA Wnt2 transfection (siWnt2) resulted in the significant inhibition of Wnt2 expression at both the mRNA and protein levels. The expression of β-catenin, GSK-3β, p-GSK-3β, and cyclin D1 at the protein level also decreased in siWnt2 cells. siWnt2 resulted in a substantially slower growth and significant delay in cell doubling time of the KFB cells compared with control groups. Further, the siRNA knock down of GSK-3β and β-catenin resulted in slower proliferation rates, respectively.Wnt2 siRNA has an inhibitive effect on keloid fibroblast proliferation, which may be a potential therapeutic approach for keloid and other human fibrotic diseases.

Modeling and Dynamic Analysis in a Hybrid Stochastic Bioeconomic System with Double Time Delays and Lévy Jumps

A double delayed hybrid stochastic prey-predator bioeconomic system with Lévy jumps is established and analyzed, where commercial harvesting on prey and environmental stochasticity on population dynamics are considered. Two discrete time delays are utilized to represent the maturation delay of prey and gestation delay of predator, respectively. For a deterministic system, positivity of solutions and uniform persistence of system are discussed. Some sufficient conditions associated with double time delays are derived to discuss asymptotic stability of interior equilibrium. For a stochastic system, existence and uniqueness of a global positive solution are studied. By using the invariant measure theory and singular boundary theory of diffusion process, existence of stochastic Hopf bifurcation and stochastic stability are investigated. By constructing appropriate Lyapunov functions, asymptotic dynamic behavior of the proposed hybrid stochastic system with double time delays and Lévy jumps is discussed. Numerical simulations are provided to show consistency with theoretical analysis.

Hopf bifurcation in time-delayed Lotka–Volterra competition systems with advection

ABSTRACTIn this paper, we study time-delayed reaction–diffusion systems with advection subject to Lotka–Volterra competition dynamics over one-dimensional domains. These systems model the population dynamics of two groups of competing species, with one dispersing randomly and the other a combination of random and biased dispersal (to avoid competition). We show that time-delay(s) in the interspecific competition mechanism can induce instability of the homogeneous equilibrium to the reaction–advection–diffusion systems, and further promote the appearance of time-oscillating spatially inhomogeneous distributions of the species. Our results indicate that these time-delayed systems (both single and double time-delays) can be used to model the well-observed time-periodic distributions of interacting species in natural fields, compared to the systems without time-delay(s).

Information-Theory-Based Complexity Quantifier for Chaotic Semiconductor Laser With Double Time Delays

The complexity properties of the chaotic signals generated by a chaotic semiconductor laser (SL) with double time delays are quantified numerically. A modified complexity quantifier, mean permutation entropy (MPE), based on information theory, is applied to fully characterize the chaotic complexity. The autocorrelation time (ACT) is also employed as a supplement quantifier. The numerical analyses of the MPE and the ACT have been performed extensively, and the effects of feedback rate, bias current, feedback delays, and linewidth enhancement factor are examined. The parameter regions leading to high chaotic complexity are identified successfully by the MPE. Besides, we also successfully quantify the chaotic complexity of the SL with three time delays. Hence, such information-theory-based MPE is an effective and universal complexity quantifier for a chaotic SL with multiple time delays, which is interesting and valuable for chaos communication systems.

Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay

This paper is devoted to the consensus problems for a fractional-order multiagent system (FOMAS) with double integral and time delay, the dynamics of which are double-integrator fractional-order model, where there are two state variables in each agent. The consensus problems are investigated for two types of the double-integrator FOMAS with time delay: the double-integrator FOMAS with time delay whose network topology is undirected topology and the double-integrator FOMAS with time delay whose network topology is directed topology with a spanning tree in this paper. Based on graph theory, Laplace transform, and frequency-domain theory of the fractional-order operator, two maximum tolerable delays are obtained to ensure that the two types of the double-integrator FOMAS with time delay can asymptotically reach consensus. Furthermore, it is proven that the results are also suitable for integer-order dynamical model. Finally, the relationship between the speed of convergence and time delay is revealed, and simulation results are presented as a proof of concept.

Nonlinear dynamic analysis on maglev train system with flexible guideway and double time-delay feedback control

In this paper, the dynamic behavior of time-delayed feedback control for maglev train system with double discrete time delays is considered with flexible guideway. Considering the maglev guideway as Beroulli-Euler beam, the mathematical model of maglev system with flexible guideway is constructed. The time delay of the two state feedback signals in the maglev system occurs simultaneously, and the values are different. The present treatment method only considers one single feedback delay, which are insufficiency. Thus, the Hopf bifurcation with double time-delay feedback of maglev train running on the flexible guideway is analyzed considering time-delayed position feedback signal τ1 and velocity feedback signal τ2. A novel method is presented to develop the double-parametric Hopf bifurcation diagram in relation to τ1 and τ2. Sufficient numerical simulations are provided to illustrate the complex dynamical behavior of the discrete delays τ1 and τ2 for maglev system and we verify the obtained theoretical analysis. Finally, the field experiments are carried out to validate the effectiveness of the Hopf bifurcation analytical method preliminarily.

Double time-delays induced stochastic dynamical characteristics for a metapopulation system subjected to the associated noises and a multiplicative periodic signal

In this paper, we aim to investigating in detail the stability of the system, the mean extinction time and stochastic resonance (SR) phenomena caused by a multiplicative periodic signal for a dual time-delayed metapopulation system subjected to cross-correlated noises. By use of the fast descent method, the small time delay approximation method and the SR theory, we obtain the expressions of the steady state probability distribution function, the mean first-passage time and signal-to-noise ratio (SNR). Numerical results indicate that the multiplicative, additive and association noises together with time delay τ can all accelerate the transition from the stable state of big density to the extinction one and play significant roles in weakening the stability and shortening the mean extinction time of the metapopulation. In particular, the additive noise and time delay τ can result in the crash of the system, while another time delay θ can strengthen the biological system stability and extend the declining time for the population. On the other hand, with respect to the SNR, the figures show that time delay τ plays entirely antipodal roles in motivating stochastic resonance (SR) in a variety of different situations. Conversely, the multiplicative noise intensity Q and time delay θ all along produce negative effect on exciting the SR. Meanwhile, the increase of the weak additive noise intensity M can stimulate the SR phenomenon, but the bigger values of M will suppress the SNR and SR phenomenon. The strength of the noise correlation λ plays an important role in restraining the SR in most cases except that it does in the plot of SNR-Q.

Dynamic analysis of a hybrid bioeconomic plankton system with double time delays and stochastic fluctuations

In this paper, we establish a double delayed hybrid bioeconomic plankton system with stochastic fluctuations and commercial harvesting on zooplankton, where maturation delay for toxin producing phytoplankton and gestation delay for zooplankton are considered. Stochastic fluctuations are incorporated into the proposed system in form of Gaussian white noises to depict stochastic environmental factors in plankton system. For deterministic system without double time delays, existence of singularity induced bifurcation is studied due to variation of economic interest of commercial harvesting, and state feedback controllers are designed to eliminate singularity induced bifurcation. For deterministic system with double time delays, positivity and uniform persistence of solutions are studied, and some sufficient conditions associated with asymptotic stability of interior equilibrium are investigated. For stochastic system without double time delays, stochastic stability and existence of stochastic Hopf bifurcation are discussed based on singular boundary theory of diffusion process and invariant measure theory. For stochastic system with double time delays, existence and uniqueness of global positive solution are investigated, and asymptotic behaviors of the interior equilibrium are studied by constructing appropriate Lyapunov functions. Numerical simulations are carried out to validate theoretical analysis.

Complex dynamics and stability analysis in a discrete hybrid bioeconomic system with double time delays

In this paper, a discrete hybrid three-species food chain system is proposed, where commercial harvesting on top predator is considered. Two time delays are introduced to represent gestation delay for prey and predator population, respectively. In absence of time delay, sufficient conditions associated with economic interest and step size are derived to show system undergoes flip bifurcation. In presence of double time delays, existence of Neimark–Sacker bifurcation and local stability switch are discussed due to variations of time delays. Furthermore, by utilizing new normal form of delayed discrete hybrid system and center manifold theorem, direction and stability of Neimark–Sacker bifurcation are studied. Numerical simulations are performed not only to validate theoretical analysis, but also exhibit cascades of period-doubling bifurcation, chaotic behavior and stable closed invariant curve.

Dynamical analysis in a bioeconomic phytoplankton zooplankton system with double time delays and environmental stochasticity

This paper presents a double delayed bioeconomic phytoplankton zooplankton system with commercial harvesting on zooplankton and environmental stochasticity. Maturation delay for toxin producing phytoplankton and gestation delay for zooplankton are considered. Environmental stochasticity is incorporated into the proposed system in form of Gaussian white noises. Some sufficient conditions are derived to show that the proposed system has a unique global positive solution. In absence of double time delays, stochastic stability and existence of stochastic Hopf bifurcation are studied based on invariant measure theory and singular boundary theory of diffusion process for the proposed system. In presence of double time delays, asymptotic behaviors of the interior equilibrium are discussed by constructing some appropriate Lyapunov functions.

Laboratory Scale Microbial Food Chain To Study Bioaccumulation, Biomagnification, and Ecotoxicity of Cadmium Telluride Quantum Dots.

The increasing applications of engineered nanomaterials (ENMs) in consumer products warrant a careful evaluation of their trophic transfer and consequent ecological impact. In the present study, a laboratory scale aquatic microbial food chain was established using bacteria (Escherichia coli (E. coli)) as a prey and ciliated protozoan (Paramecium caudatum) as a predator organism to determine the impact of cadmium telluride quantum dots (CdTe QDs). We observed that 29% of bacterivory potential of paramecium was lost, including an ∼12 h delay in doubling time on exposure to 25 mg/L CdTe QD (∼4 nm) as compared to control. The fluorescence based stoichiometric analysis revealed that 65% of the QDs bioaccumulated when paramecia were exposed to 25 mg/L QDs at 24 h. There was a significant (p < 0.05) increase in cellular cadmium (Cd) concentration at 24 h (306 ± 192 mg/L) as compared to 1 h (152 ± 50 mg/L). Moreover, the accumulation of Cd in E. coli (147 ± 25 mg/L) at 1 h of exposure to 25 mg/L QDs transferred 1.4 times higher Cd (207 ± 24 mg/L; biomagnification factor = 1.4) to its predator, paramecium.

Novel glyceryl glucoside is a low toxic alternative for cryopreservation agent

Glyceryl glucoside (GG, α-d-glucosyglycerol) is a natural glycerol derivative found in alcoholic drinks. Recently GG has been used as an alternative for glycerol in cosmetic products. However, the safety of using GG is still unclear. Currently, dimethyl sulfoxide (DMSO) and glycerol are wildly used in cryopreservation. Despite GG being a derivative of glycerol, the ability of GG in cryopreservation is still unknown. By using a system of Chinese Hamster Ovary cells (CHO), A549 cells and AG1522 cells, the study examined the cryoprotective effects of DMSO, glycerol and GG. Cytotoxic and genotoxic responses induced by the three chemicals were also investigated with CHO to determine the safety of GG for cosmetic products. Our data suggests that GG has great cryopresearvation ability in the concentration of 30%–40% (v/v).For cytotoxic studies, DMSO showed the highest cytotoxicity above 3% (v/v) in cell doubling time delay among three chemicals. For the acute cytotoxicity with trypan blue dye exclusion assay, GG showed stronger cell killing effect within 24 h above 4% (v/v). For the continuous cytotoxicity with colony formation assay for 7 days, DMSO showed significantly reduced clonogenic ability above 2%.In genotoxicity studies, CHO treated with glycerol at 2% concentration induced three times higher frequencies of sister chromatid exchange (SCE) than background levels. GG did not induce significant amounts of SCE compared to background. Micronuclei formation was equally observed in the 2% and above concentrations of glycerol and GG.Our data showed that GG has significant effects on cryopreservation compared to DMSO. Glycerol and GG have similar cytotoxicity effects to CHO, but glycerol induced genotoxic responses in the same concentration. Therefore, we conclude that GG may be a safer alternative compound to glycerol in cosmetic products and safer alternative to DMSO in cryopreservation.

Modeling and analysis in a prey–predator system with commercial harvesting and double time delays

A differential-algebraic prey–predator system with commercial harvesting on predator is proposed, where maturation delay for prey and gestation delay for predator are considered. Since commercial harvesting is dynamically influenced by variation of economic interest, we will investigate combined dynamic effects of double time delays and economic interest on population dynamics. Positivity of solutions and uniform persistence of system are studied. In the absence of time delay, by taking economic interest as bifurcation parameter, existence of singularity induced bifurcation is investigated based on differential-algebraic system theory. State feedback controllers are designed to eliminate singularity induced bifurcation and stabilize the proposed system around corresponding interior equilibrium. In the presence of double time delays, by analyzing associated characteristic transcendental equation, it is found that interior equilibrium loses local stability when double time delays cross corresponding critical values. According to Hopf bifurcation theorem for functional differential equation, existence of Hopf bifurcation is investigated as local stability switches. Based on normal form theory and center manifold theorem, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied. Numerical simulations are carried out to show consistency with theoretical analysis.

Sirs Model with Double Time Delay

This paper is concerned with the study of two SIRS Model with Double Time Delay by incorporating time delay in both infective and recovered class. In model I, we have obtained the existence of disease free and endemic equilibrium points. For Model I, by analyzing the eigenvalues of associated characteristic equation of system, the conditions ensuring the local stability of the equilibrium points are obtained. Further, for the Model II the dynamical behavior of the endemic equilibrium is shown from the point of view of stability switches aspects. Finally, numerical simulations have been carried out in support of our result.

Optimal Harvest Control in a Singular Prey-Predator Fishery Model with Maturation Delay and Gestation Delay

This paper presents a singular prey-predator fishery model, where maturation delay for prey and gestation delay for predator are considered. Fishing efforts are introduced to harvest prey and predator population, which are developed as control instruments to investigate optimal utilization of fishery resource. By analyzing associated characteristic equation, local stability analysis is studied due to combined variations of double time delays. Furthermore, Pontryagin’s maximum principle is utilized to characterize optimal harvest control, and the optimality system is numerically solved based on an iterative method.

Evolving Early Lung Cancers Detected During Follow-Up of Idiopathic Interstitial Pneumonia: Serial CT Features.

The purpose of this study was to evaluate the CT characteristics of newly developed lung cancer on CT studies obtained during follow-up of idiopathic interstitial pneumonia (IIP) before the appearance of identifiable tumors to the time of detectable lung cancer and thereafter. The study sample included 66 cancers diagnosed in 63 patients with IIP and lung cancer (59 men, four women; median age, 64 years; range, 40-85 years) between October 1998 and July 2012. Two radiologists independently reviewed 193 CT scans, determined the earliest presence of cancer and IIP, and evaluated tumor size, lobar and axial location, shape, and tumor density. Delay in clinical diagnosis and doubling time were measured with first and second follow-up CT examinations. Interobserver agreement was good (κ > 0.77). The median tumor size was 17 mm (range, 5-30 mm) for the 46 T1a and 20 T1b cancers. Most of the tumors (42 [63.6%]) were located in the lower lobes. Thirty-five tumors (53.0%) were at the interface between fibrotic cyst and normal lung, and 21 (31.8%) were in the midst of fibrotic lung cysts. Most of the tumors had a round or oval shape (52 [78.8%]) and were solid (62 [93.9%]). The median delay in diagnosis was 46 days (range, 8-760 days). The first median doubling time was 77 days (range, 15-525 days), and the second was 53 days (27-248). New lung cancers during CT follow-up of IIP usually appear as small solid nodules with a round or oval shape. Most cancers are located at the interface between fibrotic cyst and normal lung or in the midst of fibrotic cysts of the lower lobes of subpleural lung.

Research of Multiple Sensors Adaptive Fault-Tolerant Control Based on T-S Fuzzy Model for EMB System

In the electro mechanical brake (EMB) system, an improvement of the fault-tolerant control, like invalid protections of sensors and electric systems are the key problems to the development of electric vehicles. The adaptive fault-tolerant control in this paper is focus on the descriptor nonlinear system which contains double time-delays and parameter uncertainties. In fault detection and estimation, construct the controlled system model which contains multi-sensor, double time-delays and parameter uncertainties based on T-S fuzzy model, then design the observer to realize fault detection and estimation in real-time. In building the fault-tolerant control model, the first step is to choose an appropriate sliding surface, and combine the algorithm of sliding control with adaptive generic model control. Then apply the state observer to the designed sliding adaptive generic model, and build the decision model with dynamic fault reconfiguration. And the goal of this paper about the adaptive robust fault-tolerant control for the complex nonlinear controller system is achieved. Numerical SIMULINK simulation examples are given to illustrate the application and the effectiveness of the proposed design method.