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Lansun Chen

Publications and source records attributed to Lansun Chen.

12 recordsLinked to original sources
PubMed2006

Pest management through continuous and impulsive control strategies.

In this paper, we propose two mathematical models concerning continuous and, respectively, impulsive pest control strategies. In the case in which a continuous control is used, it is shown that the model admits a globally asymptotically stable positive equilibrium under appropriate conditions which involve parameter estimations. As a result, the global asymptotic stability of the unique positive equilibrium is used to establish a procedure to maintain the pests at an acceptably low level in the long term. In the case in which an impulsive control is used, it is observed that there exists a globally asymptotically stable susceptible pest-eradication periodic solution on condition that the amount of infective pests released periodically is larger than some critical value. When the amount of infective pests released is less than this critical value, the system is shown to be permanent, which implies that the trivial susceptible pest-eradication solution loses its stability. Further, the existence of a nontrivial periodic solution is also studied by means of numerical simulation. Finally, the efficiency of continuous and impulsive control policies is compared.

Algorithms↗
PubMed2006

Impulsive vaccination of an SEIRS model with time delay and varying total population size.

Pulse vaccination is an effective and important strategy for the elimination of infectious diseases. A delayed SEIRS epidemic model with pulse vaccination and varying total population size is proposed in this paper. We point out, if R* < 1, the infectious population disappear so the disease dies out, while if R(*) > 1, the infectious population persist. Our results indicate that a long period of pulsing or a small pulse vaccination rate is sufficient condition for the permanence of the model.

Communicable Diseases↗
PubMed2006

Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays.

This paper studies a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are "profitless". Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka-Volterra systems.

Animals↗
PubMed2006

Analysis of a delayed epidemic model with pulse vaccination and saturation incidence.

Pulse vaccination is an important strategy for the elimination of infectious diseases. An SEIRS epidemic model with time delays and pulse vaccination is formulated in this paper. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic system and prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger than theta*. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than theta*. The permanence of the model is investigated analytically. Our results indicate that a long latent period of the disease is sufficient condition for the extinction of the disease.

Disease Outbreaks↗
PubMed2005

Extinction and permanence of one-prey multi-predators of Holling type II function response system with impulsive biological control.

In this paper, one investigates the dynamic behaviors of one-prey multi-predator model with Holling type II functional response by introducing impulsive biological control strategy (periodic releasing natural enemies at different fixed time). By using Floquet theorem and small amplitude perturbation method, it is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value and permanence condition is established via the method of comparison involving multiple Liapunov functions. It is shown that multi-predator impulsive control strategy is more effective than the classical and single one.

Animals↗
PubMed2005

Integrated pest management models and their dynamical behaviour.

Two impulsive models of integrated pest management (IPM) strategies are proposed, one with fixed intervention times and the other with these unfixed. The first model allows natural enemies to survive but under some conditions may lead to extinction of the pest. We use a simple prey-dependent consumption model with fixed impulsive effects and show that there exists a globally stable pest-eradication periodic solution when the impulsive period is less than certain critical values. The effects of pest resistance to pesticides are also studied. The second model is constructed in the light of IPM practice such that when the pest population reaches the economic injury level (EIL), a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is invoked. Using analytical methods, we show that there exists an orbitally asymptotically stable periodic solution with a maximum value no larger than the given Economic Threshold (ET). The complete expression for this periodic solution is given and the ET is evaluated for given parameters. We also show that in some cases control costs can be reduced by replacing IPM interventions at unfixed times with periodic interventions. Further, we show that small perturbations of the system do not affect the existence and stability of the periodic solution. Thus, we provide the first demonstration using mathematical models that an IPM strategy is more effective than classical control methods.

Agriculture↗
PubMed2004

The periodic competing Lotka-Volterra model with impulsive effect.

In this paper, the dynamic behaviour of a classical periodic Lotka-Volterra competing system with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equations, some conditions are obtained for the linear stability of the trivial and semi-trivial periodic solutions. It is proved that the system can be permanent if all the trivial and semi-trivial periodic solutions are linearly unstable. We use standard bifurcation theory to show the existence of nontrivial periodic solutions which arise near the semi-trivial periodic solution. As an application, a fish harvest problem is considered. We explain how two competing species, one of which in a periodic environment without impulsive effect would be doomed to extinction, can coexist with suitably periodic impulsive harvesting.

Animals↗
PubMed2003

The effect of seasonal harvesting on stage-structured population models.

In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. We propose an exploited single-species model with stage structure for the dynamics in a fish population for which births occur in a single pulse once per time period. Since birth pulse populations are often characterized with a discrete time dynamical system determined by its Poincaré map, we explore the consequences of harvest timing to equilibrium population sizes under seasonal dependence and obtain threshold conditions for their stability, and show that the timing of harvesting has a strong impact on the persistence of the fish population, on the volume of mature fish stock and on the maximum annual-sustainable yield. Moreover, our results imply that the population can sustain much higher harvest rates if the mature fish is removed as early in the season (after the birth pulse) as possible. Further, the effects of harvesting effort and harvest timing on the dynamical complexity are also investigated. Bifurcation diagrams are constructed with the birth rate (or harvesting effort or harvest timing) as the bifurcation parameter, and these are observed to display rich structure, including chaotic bands with periodic windows, pitch-fork and tangent bifurcations, non-unique dynamics (meaning that several attractors coexist) and attractor crisis. This suggests that birth pulse, in effect, provides a natural period or cyclicity that makes the dynamical behavior more complex.

Algorithms↗
PubMed2003

Impulsive control strategies in biological control of pesticide.

By presenting and analyzing the pest-predator model under insecticides used impulsively, two impulsive strategies in biological control are put forward. The first strategy: the pulse period is fixed, but the proportional constant E(1) changes, which represents the fraction of pests killed by applying insecticide. For this scheme, two thresholds, E(1)(**) and E(1)(*) for E(1) are obtained. If E(1)>or=E(1)(*), both the pest and predator (natural enemies) populations go to extinction. If E(1)(**)<E(1)<E(1)(*), the pest population converges to the semi-trivial periodic solution while the predator population tends to zero. If E(1) is less than E(1)(**) but even if close to E(1)(**), there exists a unique positive periodic solution via bifurcation, which implies both the pest and the predator populations oscillate with a positive amplitude. In this case, pest population is killed to the maximum extent while the natural enemies are preserved to avoid extinction. The second strategy: the proportional constant E(1) is fixed (E(1)<E(1)(*) firstly), but the pulse period changes. For this scheme, one threshold tau(0) for the pulse period tau is obtained. We can reach the same target as above by controlling the period impulsive effect tau<tau(0), even if close to tau(0). Our theoretical results are confirmed by numerical simulations.

Animals↗
PubMed2003

Multiple attractors in stage-structured population models with birth pulses.

In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. A single species stage-structured model with density-dependent maturation rate and birth pulse is formulated. Using the discrete dynamical system determined by its Poincaré map, we report a detailed study of the various dynamics, including (a) existence and stability of nonnegative equilibria, (b) nonunique dynamics, meaning that several attractors coexist, (c) basins of attraction (defined as the set of the initial conditions leading to a certain type of attractor), (d) supertransients, and (e) chaotic attractors. The occurrence of these complex dynamic behaviour is related to the fact that minor changes in parameter or initial values can strikingly change the dynamic behaviours of system. Further, it is shown that periodic birth pulse, in effect, provides a natural period or cyclicity that allows multiple oscillatory solutions in the continuous dynamical systems.

Animals↗
PubMed2003

Extinction and permanence of a two-prey one-predator system with impulsive effect.

In this paper, we investigate a two-prey one-predator system with impulsive effect on the predator of fixed moment. By using Floquet's theorem and small-amplitude perturbation skills, we show that there exists a globally asymptotically stable two-pest eradication periodic solution when the impulsive period is less than some critical value. Further, we prove that the system is permanent if the impulsive period is larger than some critical value, and meanwhile the conditions for the extinction of one of the two prey and permanence of the remaining two species are given. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level. Therefore, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels.

Animals↗
PubMed2002

Density-dependent birth rate, birth pulses and their population dynamic consequences.

In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. We propose a single-species model with stage structure for the dynamics in a wild animal population for which births occur in a single pulse once per time period. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact periodic solution of systems which are with Ricker functions or Beverton-Holt functions, and obtain the threshold conditions for their stability. Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behaviors of the single species model with birth pulses are very complex, including small-amplitude annual oscillations, large-amplitude multi-annual cycles, and chaos. This suggests that birth pulse, in effect, provides a natural period or cyclicity that allows for a period-doubling route to chaos.

Animals↗