Hunki Baek

Species extinction and permanence of an impulsively controlled two-prey one-predator system with seasonal effects

Recently, the population dynamic systems with impulsive controls have been researched by many authors. However, most of them are reluctant to study the seasonal effects on prey. Thus, in this paper, an impulsively controlled two-prey one-predator system with the Beddington-DeAngelis type functional response and seasonal effects is investigated. By using the Floquet theory, the sufficient conditions for the existence of a globally asymptotically stable two-prey-free periodic solution are established. Further, it is proven that this system is permanent under some conditions via a comparison method involving multiple Lyapunov functions and meanwhile the conditions for extinction of one of the two prey and permanence of the remaining two species are given.

A food chain system with Holling type IV functional response and impulsive perturbations

In this paper, a three-trophic-level food chain system with Holling type IV functional response and impulsive perturbations is established. We show that this system is uniformly bounded. Using the Floquet theory of impulsive equations and small perturbation skills, we find conditions for the local and global stabilities of the prey and top predator-free periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent via the comparison theorem. We display some numerical examples to substantiate our theoretical results.

PERMUTATION ENTROPY APPLIED TO MOVEMENT BEHAVIORS OF DROSOPHILA MELANOGASTER

Movement of different strains in Drosophila melanogaster was continuously observed by using computer interfacing techniques and was analyzed by permutation entropy (PE) after exposure to toxic chemicals, toluene (0.1 mg/m3) and formaldehyde (0.01 mg/m3). The PE values based on one-dimensional time series position (vertical) data were variable according to internal constraint (i.e. strains) and accordingly increased in response to external constraint (i.e. chemicals) by reflecting diversity in movement patterns from both normal and intoxicated states. Cross-correlation function revealed temporal associations between the PE values and between the component movement patterns in different chemicals and strains through the period of intoxication. The entropy based on the order of position data could be a useful means for complexity measure in behavioral changes and for monitoring the impact of stressors in environment.

Extinction and Permanence of a Three-Species Lotka-Volterra System with Impulsive Control Strategies

A three-species Lotka-Volterra system with impulsive control strategies containing the biological control (the constant impulse) and the chemical control (the proportional impulse) with the same period, but not simultaneously, is investigated. By applying the Floquet theory of impulsive differential equation and small amplitude perturbation techniques to the system, we find conditions for local and global stabilities of a lower-level prey and top-predator free periodic solution of the system. In addition, it is shown that the system is permanent under some conditions by using comparison results of impulsive differential inequalities. We also give a numerical example that seems to indicate the existence of chaotic behavior.

A Three-Species Food Chain System with Two Types of Functional Responses

In recent decades, many researchers have investigated the ecological models with three and more species to understand complex dynamical behaviors of ecological systems in nature. However, when they studied the models with three species, they have just considered the functional responses between prey and mid-predator and between mid-predator and top predator as the same type. However, in the paper, in order to describe more realistic ecological world, a three-species food chain system with two types of functional response, Holling type and Beddington-DeAngelis type, is considered. It is shown that this system is dissipative. Also, the local and global stability of equilibrium points of the system is established. In addition, conditions for the persistence of the system are found according to the existence of limit cycles. Some numerical examples are given to substantiate our theoretical results. Moreover, we provide numerical evidence of the existence of chaotic phenomena by illustrating bifurcation diagrams of system and by calculating the largest Lyapunov exponent.

Analysis of an Impulsive Predator-Prey System with Monod-Haldane Functional Response and Seasonal Effects

For a class of impulsive predator-prey systems with Monod-Haldane functional response and seasonal effects, we investigate conditions for the local and global stabilities of prey-free solutions and for the permanence of the system by using the Flquet theory of impulsive differential equations and comparison techniques. In addition, we numerically analyze the phenomena caused by seasonal effects and impulsive perturbation. It will be applicable to the controllability for the population of prey and predator.

Stability for a Holling Type IV Food Chain System With Impulsive Perturbations

Abstract. We investigate a three species food chain system with a Holling type IVfunctional response and impulsive perturbations. We find conditions for local and globalstabilities of prey(or predator) free periodic solutions by applying the Floquet theory andthe comparison theorems. 1. IntroductionIt is currently very much in vogue to study population models with impulsiveperturbations containing biological and chemical controls. Especially, simple multi-species systems consisting of a three species food chain with impulsive perturbationshave been discussed by a number of researchers [13], [17], [18], [19], [20] and thereare also many literatures on impulsive prey-predator population models [10], [11],[12].A well-known model of such systems is a food chain system with Holling typeIV functional response [7], [14], [20], which can be described the following equation:(1.1)x 0 (t) = x(t)(a−bx(t))−c 1 x(t)y(t)1+e 1 x 2 (t),y 0 (t) = −d 1 y(t)+c 2 x(t)y(t)1+e 1 x 2 (t)−c 3 y(t)z(t)1+e

Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion

We investigate spatiotemporal dynamics of a semi-ratio-dependent predator-prey system with reaction-diffusion and zero-flux boundary. We obtain the conditions for Hopf, Turing, and wave bifurcations of the system in a spatial domain by making use of the linear stability analysis and the bifurcation analysis. In addition, for an initial condition which is a small amplitude random perturbation around the steady state, we classify spatial pattern formations of the system by using numerical simulations. The results of numerical simulations unveil that there are various spatiotemporal patterns including typical Turing patterns such as spotted, spot-stripelike mixtures and stripelike patterns thanks to the Turing instability, that an oscillatory wave pattern can be emerged due to the Hopf and wave instability, and that cooperations of Turing and Hopf instabilities can cause occurrence of spiral patterns instead of typical Turing patterns. Finally, we discuss spatiotemporal dynamics of the system for several different asymmetric initial conditions via numerical simulations.

Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations

We study a Beddington-DeAngelis type predator-prey system with impulsive perturbation and seasonal effects. First, we numerically observe the influence of seasonal effects on the system without impulsive perturbations. Next, we find the conditions for the local and global stabilities of prey-free periodic solutions by using Floquet theory for the impulsive equation and small amplitude perturbation skills, and for the permanence of the system via comparison theorem. Finally, we show that seasonal effects and impulsive perturbation can give birth to various kinds of dynamical behavior of the system including chaotic phenomena by numerical simulations.

Permanence of a Three-species Food Chain System with Impulsive Perturbations

We investigate a three-species food chain system with Lotka-Volterra func- tional response and impulsive perturbations. In (23), Zhang and Chen have studied the system. They have given conditions for extinction of lowest-level prey and top predator and considered the local stability of lower-level prey and top predator eradication periodic solution. However, they did not give a condition for permanence, which is one of important facts in population dynamics. In this paper, we establish the condition for permanence of the three-species food chain system with impulsive perturbations. In addition, we give some numerical examples.