Levulinic acid(LA) has been identified as a promising green,biomass derived platform chemical.Response surface analysis(RSA) with a four-factor-five-level central composite design(CCD) was applied to optimize th...Levulinic acid(LA) has been identified as a promising green,biomass derived platform chemical.Response surface analysis(RSA) with a four-factor-five-level central composite design(CCD) was applied to optimize the hydrolysis conditions for the conversion of bamboo(Phyllostachys Praecox f.preveynalis) shoot shell(BSS) to LA catalyzed with ionic liquid [C4mim]HSO4.The effects of four main reaction parameters including temperature,time,C[C4mim]HSO4(initial [C4mim]HSO4 concentration) and XBSS(initial BSS intake) on the hydrolysis reaction for yield of LA were analyzed.A quadratic equation model for yield of LA was established and fitted to the data with an R2 of 0.9868,and effects of main factors and their corresponding relationships were obtained with RSA.Model validation and results of CCD showed good correspondence between actual and predicted values.The analysis of variance(ANOVA) of the results indicated that the yield of LA in the range studied was significantly(P<0.05) affected by the four factors.The optimized reaction conditions were as follows:temperature of 145 ℃,time of 103.8 min,C[C4mim]HSO4 of 0.9 mol.L-1 and XBSS of 2.04%(by mass),respectively.A high yield [(71±0.41)%(by mol),triplicate experiment] was obtained at the optimum conditions of temperature of 145 ℃,time of 104 min,C[C4mim]HSO4 of 0.9 mol.L-1 and XBSS of 2%(by mass),which obtained from the real experiments,concurred with the model prediction [73.8%(by mol) based on available C6 sugars in BSS or 17.9%(by mass) based on the mass of BSS],indicating that the model was adequate for the hydrolysis process.展开更多
We consider differentiated timecritical task scheduling in a N×N input queued optical packet s w itch to ens ure 100% throughput and meet different delay requirements among various modules of data center. Existin...We consider differentiated timecritical task scheduling in a N×N input queued optical packet s w itch to ens ure 100% throughput and meet different delay requirements among various modules of data center. Existing schemes either consider slot-by-slot scheduling with queue depth serving as the delay metric or assume that each input-output connection has the same delay bound in the batch scheduling mode. The former scheme neglects the effect of reconfiguration overhead, which may result in crippled system performance, while the latter cannot satisfy users' differentiated Quality of Service(Qo S) requirements. To make up these deficiencies, we propose a new batch scheduling scheme to meet the various portto-port delay requirements in a best-effort manner. Moreover, a speedup is considered to compensate for both the reconfiguration overhead and the unavoidable slots wastage in the switch fabric. With traffic matrix and delay constraint matrix given, this paper proposes two heuristic algorithms Stringent Delay First(SDF) and m-order SDF(m-SDF) to realize the 100% packet switching, while maximizing the delay constraints satisfaction ratio. The performance of our scheme is verified by extensive numerical simulations.展开更多
The resource allocation problem in data centre networks refers to a map of the workloads provided by the cloud users/tenants to the Substrate Network(SN)which are provided by the cloud providers.Existing studies consi...The resource allocation problem in data centre networks refers to a map of the workloads provided by the cloud users/tenants to the Substrate Network(SN)which are provided by the cloud providers.Existing studies consider the dynamic arrival and departure of the workloads,while the dynamics of the substrate are ignored.In this paper,we first propose the resource allocation with the dynamic SN,and denote it as GraphMap-DS.Then,we propose an efficient mapping algorithm for GraphMap-DS.The performance of the proposed algorithm is evaluated by performing simulation experiments.Our results show that the proposed algorithm can effectively solve the GraphMap-DS.展开更多
MapReduce has emerged as a popular computing model used in datacenters to process large amount of datasets.In the map phase,hash partitioning is employed to distribute data that sharing the same key across data center...MapReduce has emerged as a popular computing model used in datacenters to process large amount of datasets.In the map phase,hash partitioning is employed to distribute data that sharing the same key across data center-scale cluster nodes.However,we observe that this approach can lead to uneven data distribution,which can result in skewed loads among reduce tasks,thus hamper performance of MapReduce systems.Moreover,worker nodes in MapReduce systems may differ in computing capability due to(1) multiple generations of hardware in non-virtualized data centers,or(2) co-location of virtual machines in virtualized data centers.The heterogeneity among cluster nodes exacerbates the negative effects of uneven data distribution.To improve MapReduce performance in heterogeneous clusters,we propose a novel load balancing approach in the reduce phase.This approach consists of two components:(1) performance prediction for reducers that run on heterogeneous nodes based on support vector machines models,and(2) heterogeneity-aware partitioning(HAP),which balances skewed data for reduce tasks.We implement this approach as a plug-in in current MapReduce system.Experimental results demonstrate that our proposed approach distributes work evenly among reduce tasks,and improves MapReduce performance with little overhead.展开更多
Background Submaximal oxygen uptake measures are more feasible and may better predict clinical cardiac outcomes than maximal tests in older adults with heart failure (HF). We examined relationships between maximal o...Background Submaximal oxygen uptake measures are more feasible and may better predict clinical cardiac outcomes than maximal tests in older adults with heart failure (HF). We examined relationships between maximal oxygen uptake, submaximal oxygen kinetics, fianctional mobility, and physical activity in older adults with HF and reduced ejection fraction. Methods Older adults with HF and reduced ejection fraction (n = 25, age 75 :i: 7 years) were compared to 25 healthy ageand gender-matched controls. Assessments included a maximal treadmill test for peak oxygen uptake (VO2p^ak), oxygen uptake kinetics at onset of and on recovery from a submaximal treadmill test, functional mobility testing [Get Up and Go (GUG), Comfortable Gait Speed (CGS), Unipedal Stance (US)], and self-reported physical activity (PA). Results Compared to controls, HF had worse performance on GUG, CGS, and US, greater delays in submaximal oxygen uptake kinetics, and lower PA. In controls, VO2peak was more strongly associated with functional mobility and PA than submaximal oxygen uptake kinetics. In HF patients, submaximal oxygen uptake kinetics were similarly associated with GUG and CGS as VO2peak, but weakly associated with PA. Conclusions Based on their mobility performance, older HF patients with reduced ejection fraction are at risk for adverse functional outcomes. In this population, submaximal oxygen uptake measures may be equivalent to VO2 peak in predicting functional mobility, and in addition to being more feasible, may provide better insight into how aerobic function relates to mobility in older adults with HF.展开更多
Cloud computing provides the essential infrastructure for multi-tier Ambient Assisted Living(AAL) applications that facilitate people's lives. Resource provisioning is a critically important problem for AAL applic...Cloud computing provides the essential infrastructure for multi-tier Ambient Assisted Living(AAL) applications that facilitate people's lives. Resource provisioning is a critically important problem for AAL applications in cloud data centers(CDCs). This paper focuses on modeling and analysis of multi-tier AAL applications, and aims to optimize resource provisioning while meeting requests' response time constraint. This paper models a multi-tier AAL application as a hybrid multi-tier queueing model consisting of an M/M/c queueing model and multiple M/M/1 queueing models. Then, virtual machine(VM) allocation is formulated as a constrained optimization problem in a CDC, and is further solved with the proposed heuristic VM allocation algorithm(HVMA). The results demonstrate that the proposed model and algorithm can effectively achieve dynamic resource provisioning while meeting the performance constraint.展开更多
Advancement of the information society has proceeded with the development of information and communication technology, and a demand on a data center has increased. In such a situation, the number of servers is increas...Advancement of the information society has proceeded with the development of information and communication technology, and a demand on a data center has increased. In such a situation, the number of servers is increasing in a data center. Thus, the heat density in a data center is much higher than that of usual offices. And typically, almost 40% of the total power consumption is used for cooling servers in a data center. Thus, cooling effectiveness is one of the most important factors in evaluating the value of the data center. The data center taken up in this paper is located in Ishikari, where is a cold district in Japan. Using the cool outdoor air for cooling servers helps us to cut the power consumption for cooling. This paper first assesses the efficiency of Ishikari data center measuring the temperature of seven parts in a building where the cooling air flowing. Second, this paper describes the most efficient method for the operation and estimates 1.11 of PUE (power usage effectiveness).展开更多
Taking into account stealth, structure and maintenance, ultra-compact S-shaped intake has been widely used in modem vehicles. In this paper a series of steady numerical simulation were carried out to investigate the c...Taking into account stealth, structure and maintenance, ultra-compact S-shaped intake has been widely used in modem vehicles. In this paper a series of steady numerical simulation were carried out to investigate the complex flow mechanism in s-shaped intake, particular attention was given to examining the effect of centerline curvature on the performance and flowfield of an ultra-compact S-shaped intake. In order to validate the multi-block model, the computational results for Royal Aircraft Establishment intake 2129-M2129 which had modest centerline cur- vature distribution were corrected with available experimental test data. The numerical simulation results agreed fairly well with the experimental data, and the computational method was then used to investigate the effects of different centerline curvature distributions on performance and flow field in compact S-shaped intake. Detailed analyses of the flow visualization had exposed the different flow topologies between the cases with different cen- terline curvature. It was found that different centerline curvature distributions changed the initial location and the size of separation bubble, as well as the strength of two counter-rotating vortices at the entrance of engine.展开更多
OBJECTIVE: To investigate on Left ventricular ejection fraction value and aldosterone of two medicinals of Traditional Chinese Medicine(TCM) with the properties of warming Yang and tonifying Qi in terms of TCM theory....OBJECTIVE: To investigate on Left ventricular ejection fraction value and aldosterone of two medicinals of Traditional Chinese Medicine(TCM) with the properties of warming Yang and tonifying Qi in terms of TCM theory.METHODS: An animal model of coronary ligation of heart failure after myocardial infarction was employed to study the influence of these two kinds of drugs on three batches of rats. On the basis of the average score of left ventricle ejection fraction during the investigation, there were some different groups, including Wen Yang(the warming Yang)group, Yi Qi(tonifying Qi) group, Wen Yang and Yi Qi group, captopril group, digoxin group. In additional, an artificial operation group was set for compari-son. The systemic intervention using these medicinal and drugs was taken effects on the 2nd day after the operation of myocardial infraction(MI) with once a day. At week one, two, and four after the MI treatment, evaluated were EF values, and ferritin,angiotensin-II and aldosterone in the rats' plasma.RESULTS: At week one and week two, the medicinal of Wen Yang, Yi Qi, Wen Yang pluse Yi Qi, and digoxin could improve left ventricular ejection fraction in rats with heart failure; Compared to the model group, captopril Left ventricular EF value increased, but there was not significant. At week four,heart failure and left ventricular EF values was improved in the intervention group and the other four captopril drug intervention. At week one in the rats with drug intervention, the medicinals of Yi Qi, Wen Yang plus Yi Qi, and captopril could inhibit activation in vivo hormone aldosterone in heart failure rats; aldosterone in Wen Yang group and digoxin group were not different from that in the model group at week two and four.CONCLUSION: Chinese medicinals with properties of Wen Yang, Yi Qi have significant effect on improving left ventricular EF in rats with heart failure; compared to Yi Qi medicinals, Wen Yang medicinals that inhibit the effectiveness of the time required for the activation of the role of aldosterone. The medicinals of Wen Yang and Yi Qi seems better by inhibiting the activation of the hormone aldosterone after failing to inhibit ventricular remodeling to improve heart failure.展开更多
In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and...In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and discrete delay are studied. The Hopf bifurcations can be shown when the delay crosses the critical value. Furthermore, based on the normal form and the center manifold theorem, the type, stability and other properties of the bifurcating periodic solutions are determined. Finally, some numerical simulations are given to illustrate the results.展开更多
A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multip...A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.展开更多
In this paper, we study dynamics in a predator-prey model with delay, in which predator can be infected, with particular attention focused on nonresonant double Hopf bifurca- tion. By using center manifold reduction m...In this paper, we study dynamics in a predator-prey model with delay, in which predator can be infected, with particular attention focused on nonresonant double Hopf bifurca- tion. By using center manifold reduction methods, we obtain the equivalent normal forms near a double Hopf critical point in this system. Moreover, bifurcations are classified in a two-dimensional parameter space near the critical point. Numerical simulations are presented to demonstrate the applicability of the theoretical results.展开更多
基金Supported by the National Natural Science Foundation of China(30940058,31170672)the Natural Science Foundation of Zhejiang Province of China(Y3110025)+1 种基金Key Laboratory for Physical Processing of Agricultural Products(JAPP2010-4)Key Laboratory of Exploitation and Preservation of Coastal Bio-resource(2010F30003)
文摘Levulinic acid(LA) has been identified as a promising green,biomass derived platform chemical.Response surface analysis(RSA) with a four-factor-five-level central composite design(CCD) was applied to optimize the hydrolysis conditions for the conversion of bamboo(Phyllostachys Praecox f.preveynalis) shoot shell(BSS) to LA catalyzed with ionic liquid [C4mim]HSO4.The effects of four main reaction parameters including temperature,time,C[C4mim]HSO4(initial [C4mim]HSO4 concentration) and XBSS(initial BSS intake) on the hydrolysis reaction for yield of LA were analyzed.A quadratic equation model for yield of LA was established and fitted to the data with an R2 of 0.9868,and effects of main factors and their corresponding relationships were obtained with RSA.Model validation and results of CCD showed good correspondence between actual and predicted values.The analysis of variance(ANOVA) of the results indicated that the yield of LA in the range studied was significantly(P<0.05) affected by the four factors.The optimized reaction conditions were as follows:temperature of 145 ℃,time of 103.8 min,C[C4mim]HSO4 of 0.9 mol.L-1 and XBSS of 2.04%(by mass),respectively.A high yield [(71±0.41)%(by mol),triplicate experiment] was obtained at the optimum conditions of temperature of 145 ℃,time of 104 min,C[C4mim]HSO4 of 0.9 mol.L-1 and XBSS of 2%(by mass),which obtained from the real experiments,concurred with the model prediction [73.8%(by mol) based on available C6 sugars in BSS or 17.9%(by mass) based on the mass of BSS],indicating that the model was adequate for the hydrolysis process.
基金supported by the Major State Basic Research Program of China (973 project No. 2013CB329301 and 2010CB327806)the Natural Science Fund of China (NSFC project No. 61372085, 61032003, 61271165 and 61202379)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China (RFDP project No. 20120185110025, 20120185110030 and 20120032120041)supported by Tianjin Key Laboratory of Cognitive Computing and Application, School of Computer Science and Technology, Tianjin University, Tianjin, P. R. China
文摘We consider differentiated timecritical task scheduling in a N×N input queued optical packet s w itch to ens ure 100% throughput and meet different delay requirements among various modules of data center. Existing schemes either consider slot-by-slot scheduling with queue depth serving as the delay metric or assume that each input-output connection has the same delay bound in the batch scheduling mode. The former scheme neglects the effect of reconfiguration overhead, which may result in crippled system performance, while the latter cannot satisfy users' differentiated Quality of Service(Qo S) requirements. To make up these deficiencies, we propose a new batch scheduling scheme to meet the various portto-port delay requirements in a best-effort manner. Moreover, a speedup is considered to compensate for both the reconfiguration overhead and the unavoidable slots wastage in the switch fabric. With traffic matrix and delay constraint matrix given, this paper proposes two heuristic algorithms Stringent Delay First(SDF) and m-order SDF(m-SDF) to realize the 100% packet switching, while maximizing the delay constraints satisfaction ratio. The performance of our scheme is verified by extensive numerical simulations.
基金supported by the National Basic Research of China(973 Program)under Grant No.2011CB302601the National Natural Science Foundation of China under Grants No.90818028,No.6903043,No.61202117the National High Technology Research and Development Program of China(863 Program)under Grant No.2012AA011201
文摘The resource allocation problem in data centre networks refers to a map of the workloads provided by the cloud users/tenants to the Substrate Network(SN)which are provided by the cloud providers.Existing studies consider the dynamic arrival and departure of the workloads,while the dynamics of the substrate are ignored.In this paper,we first propose the resource allocation with the dynamic SN,and denote it as GraphMap-DS.Then,we propose an efficient mapping algorithm for GraphMap-DS.The performance of the proposed algorithm is evaluated by performing simulation experiments.Our results show that the proposed algorithm can effectively solve the GraphMap-DS.
基金The authors would like to thank the reviewers for their detailed reviews and constructive comments, which have helped improve the quality of this paper. This work is support- ed by National High-Tech Research and Development Plan of China under grants NO.2011AA01A204, and 2012AA01A306, National Natural Science Foundation of China under grant NO. 61202041, and NO.91330117.
文摘MapReduce has emerged as a popular computing model used in datacenters to process large amount of datasets.In the map phase,hash partitioning is employed to distribute data that sharing the same key across data center-scale cluster nodes.However,we observe that this approach can lead to uneven data distribution,which can result in skewed loads among reduce tasks,thus hamper performance of MapReduce systems.Moreover,worker nodes in MapReduce systems may differ in computing capability due to(1) multiple generations of hardware in non-virtualized data centers,or(2) co-location of virtual machines in virtualized data centers.The heterogeneity among cluster nodes exacerbates the negative effects of uneven data distribution.To improve MapReduce performance in heterogeneous clusters,we propose a novel load balancing approach in the reduce phase.This approach consists of two components:(1) performance prediction for reducers that run on heterogeneous nodes based on support vector machines models,and(2) heterogeneity-aware partitioning(HAP),which balances skewed data for reduce tasks.We implement this approach as a plug-in in current MapReduce system.Experimental results demonstrate that our proposed approach distributes work evenly among reduce tasks,and improves MapReduce performance with little overhead.
文摘Background Submaximal oxygen uptake measures are more feasible and may better predict clinical cardiac outcomes than maximal tests in older adults with heart failure (HF). We examined relationships between maximal oxygen uptake, submaximal oxygen kinetics, fianctional mobility, and physical activity in older adults with HF and reduced ejection fraction. Methods Older adults with HF and reduced ejection fraction (n = 25, age 75 :i: 7 years) were compared to 25 healthy ageand gender-matched controls. Assessments included a maximal treadmill test for peak oxygen uptake (VO2p^ak), oxygen uptake kinetics at onset of and on recovery from a submaximal treadmill test, functional mobility testing [Get Up and Go (GUG), Comfortable Gait Speed (CGS), Unipedal Stance (US)], and self-reported physical activity (PA). Results Compared to controls, HF had worse performance on GUG, CGS, and US, greater delays in submaximal oxygen uptake kinetics, and lower PA. In controls, VO2peak was more strongly associated with functional mobility and PA than submaximal oxygen uptake kinetics. In HF patients, submaximal oxygen uptake kinetics were similarly associated with GUG and CGS as VO2peak, but weakly associated with PA. Conclusions Based on their mobility performance, older HF patients with reduced ejection fraction are at risk for adverse functional outcomes. In this population, submaximal oxygen uptake measures may be equivalent to VO2 peak in predicting functional mobility, and in addition to being more feasible, may provide better insight into how aerobic function relates to mobility in older adults with HF.
文摘Cloud computing provides the essential infrastructure for multi-tier Ambient Assisted Living(AAL) applications that facilitate people's lives. Resource provisioning is a critically important problem for AAL applications in cloud data centers(CDCs). This paper focuses on modeling and analysis of multi-tier AAL applications, and aims to optimize resource provisioning while meeting requests' response time constraint. This paper models a multi-tier AAL application as a hybrid multi-tier queueing model consisting of an M/M/c queueing model and multiple M/M/1 queueing models. Then, virtual machine(VM) allocation is formulated as a constrained optimization problem in a CDC, and is further solved with the proposed heuristic VM allocation algorithm(HVMA). The results demonstrate that the proposed model and algorithm can effectively achieve dynamic resource provisioning while meeting the performance constraint.
文摘Advancement of the information society has proceeded with the development of information and communication technology, and a demand on a data center has increased. In such a situation, the number of servers is increasing in a data center. Thus, the heat density in a data center is much higher than that of usual offices. And typically, almost 40% of the total power consumption is used for cooling servers in a data center. Thus, cooling effectiveness is one of the most important factors in evaluating the value of the data center. The data center taken up in this paper is located in Ishikari, where is a cold district in Japan. Using the cool outdoor air for cooling servers helps us to cut the power consumption for cooling. This paper first assesses the efficiency of Ishikari data center measuring the temperature of seven parts in a building where the cooling air flowing. Second, this paper describes the most efficient method for the operation and estimates 1.11 of PUE (power usage effectiveness).
文摘Taking into account stealth, structure and maintenance, ultra-compact S-shaped intake has been widely used in modem vehicles. In this paper a series of steady numerical simulation were carried out to investigate the complex flow mechanism in s-shaped intake, particular attention was given to examining the effect of centerline curvature on the performance and flowfield of an ultra-compact S-shaped intake. In order to validate the multi-block model, the computational results for Royal Aircraft Establishment intake 2129-M2129 which had modest centerline cur- vature distribution were corrected with available experimental test data. The numerical simulation results agreed fairly well with the experimental data, and the computational method was then used to investigate the effects of different centerline curvature distributions on performance and flow field in compact S-shaped intake. Detailed analyses of the flow visualization had exposed the different flow topologies between the cases with different cen- terline curvature. It was found that different centerline curvature distributions changed the initial location and the size of separation bubble, as well as the strength of two counter-rotating vortices at the entrance of engine.
基金Supported by National Natural Science Foundation of China(No.81173408)Henan University of Chinese Medicine synergy innovation center
文摘OBJECTIVE: To investigate on Left ventricular ejection fraction value and aldosterone of two medicinals of Traditional Chinese Medicine(TCM) with the properties of warming Yang and tonifying Qi in terms of TCM theory.METHODS: An animal model of coronary ligation of heart failure after myocardial infarction was employed to study the influence of these two kinds of drugs on three batches of rats. On the basis of the average score of left ventricle ejection fraction during the investigation, there were some different groups, including Wen Yang(the warming Yang)group, Yi Qi(tonifying Qi) group, Wen Yang and Yi Qi group, captopril group, digoxin group. In additional, an artificial operation group was set for compari-son. The systemic intervention using these medicinal and drugs was taken effects on the 2nd day after the operation of myocardial infraction(MI) with once a day. At week one, two, and four after the MI treatment, evaluated were EF values, and ferritin,angiotensin-II and aldosterone in the rats' plasma.RESULTS: At week one and week two, the medicinal of Wen Yang, Yi Qi, Wen Yang pluse Yi Qi, and digoxin could improve left ventricular ejection fraction in rats with heart failure; Compared to the model group, captopril Left ventricular EF value increased, but there was not significant. At week four,heart failure and left ventricular EF values was improved in the intervention group and the other four captopril drug intervention. At week one in the rats with drug intervention, the medicinals of Yi Qi, Wen Yang plus Yi Qi, and captopril could inhibit activation in vivo hormone aldosterone in heart failure rats; aldosterone in Wen Yang group and digoxin group were not different from that in the model group at week two and four.CONCLUSION: Chinese medicinals with properties of Wen Yang, Yi Qi have significant effect on improving left ventricular EF in rats with heart failure; compared to Yi Qi medicinals, Wen Yang medicinals that inhibit the effectiveness of the time required for the activation of the role of aldosterone. The medicinals of Wen Yang and Yi Qi seems better by inhibiting the activation of the hormone aldosterone after failing to inhibit ventricular remodeling to improve heart failure.
基金Acknowledgments The authors would like to thank the editors and the anonymous referees for their helpful suggestions and comments which led to the improvement of our original manuscript. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11561022, 11261017), the China Postdoctoral Science Foundation (Grant No. 2014M562008).
文摘In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and discrete delay are studied. The Hopf bifurcations can be shown when the delay crosses the critical value. Furthermore, based on the normal form and the center manifold theorem, the type, stability and other properties of the bifurcating periodic solutions are determined. Finally, some numerical simulations are given to illustrate the results.
文摘A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.
文摘In this paper, we study dynamics in a predator-prey model with delay, in which predator can be infected, with particular attention focused on nonresonant double Hopf bifurca- tion. By using center manifold reduction methods, we obtain the equivalent normal forms near a double Hopf critical point in this system. Moreover, bifurcations are classified in a two-dimensional parameter space near the critical point. Numerical simulations are presented to demonstrate the applicability of the theoretical results.