Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1771

Search results for: delayed alternate form

1771 Development and Psychometric Properties of the Relational Mobility Scale for the Indonesian Population

Authors: Sukaesi Marianti

Abstract:

This study aims to develop the Relational Mobility Scale for the Indonesian population and to investigate its psychometric properties. New items of the scale were created taking into account the Indonesian population which consists of two parallel forms (A and A’). This study uses 30 newly orchestrated items while keeping in mind the characteristics of the targeted population. The scale was administered to 433 public high school students in Malang, Indonesia. Construct validity of its factor structure was demonstrated using exploratory factor analysis and confirmatory factor analysis. The result exhibits that he model fits the data, and that the delayed alternate form method shows acceptable result. Results yielded that 21 items of the three-dimensional Relational Mobility Scale is suitable for measuring relational mobility in high school students of Indonesian population.

Keywords: Confirmatory factor analysis, exploratory factor analysis, delayed alternate form, Indonesian population, relational mobility scale.

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1770 Bifurcations of a Delayed Prototype Model

Authors: Changjin Xu

Abstract:

In this paper, a delayed prototype model is studied. Regarding the delay as a bifurcation parameter, we prove that a sequence of Hopf bifurcations will occur at the positive equilibrium when the delay increases. Using the normal form method and center manifold theory, some explicit formulae are worked out for determining the stability and the direction of the bifurcated periodic solutions. Finally, Computer simulations are carried out to explain some mathematical conclusions.

Keywords: Prototype model, Stability, Hopf bifurcation, Delay, Periodic solution.

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1769 Modeling and Stability Analysis of Delayed Game Network

Authors: Zixin Liu, Jian Yu, Daoyun Xu

Abstract:

This paper aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustrated through a delayed singular system. Combined with Finsler-s Lemma and Lyapunov stable theory, a sufficient condition guaranteeing the unique existence and stability of zero-sum game-s Nash equilibrium is derived. One numerical example is presented to illustrate the validity of the main result.

Keywords: Game networks, zero-sum game, delayed singular system, nonlinear perturbation, time delay.

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1768 Steepest Descent Method with New Step Sizes

Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

Abstract:

Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: Convergence, iteration, line search, running time, steepest descent, unconstrained optimization.

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1767 Optimal Tuning of a Fuzzy Immune PID Parameters to Control a Delayed System

Authors: S. Gherbi, F. Bouchareb

Abstract:

This paper deals with the novel intelligent bio-inspired control strategies, it presents a novel approach based on an optimal fuzzy immune PID parameters tuning, it is a combination of a PID controller, inspired by the human immune mechanism with fuzzy logic. Such controller offers more possibilities to deal with the delayed systems control difficulties due to the delay term. Indeed, we use an optimization approach to tune the four parameters of the controller in addition to the fuzzy function; the obtained controller is implemented in a modified Smith predictor structure, which is well known that it is the most efficient to the control of delayed systems. The application of the presented approach to control a three tank delay system shows good performances and proves the efficiency of the method.

Keywords: Delayed systems, Fuzzy Immune PID, Optimization, Smith predictor.

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1766 Predicting Bridge Pier Scour Depth with SVM

Authors: Arun Goel

Abstract:

Prediction of maximum local scour is necessary for the safety and economical design of the bridges. A number of equations have been developed over the years to predict local scour depth using laboratory data and a few pier equations have also been proposed using field data. Most of these equations are empirical in nature as indicated by the past publications. In this paper attempts have been made to compute local depth of scour around bridge pier in dimensional and non-dimensional form by using linear regression, simple regression and SVM (Poly & Rbf) techniques along with few conventional empirical equations. The outcome of this study suggests that the SVM (Poly & Rbf) based modeling can be employed as an alternate to linear regression, simple regression and the conventional empirical equations in predicting scour depth of bridge piers. The results of present study on the basis of non-dimensional form of bridge pier scour indicate the improvement in the performance of SVM (Poly & Rbf) in comparison to dimensional form of scour.

Keywords: Modeling, pier scour, regression, prediction, SVM (Poly & Rbf kernels).

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1765 Ecotoxicity Evaluation and Suggestion of Remediation Method of ZnO Nanoparticles in Aqueous Phase

Authors: Hyunsang Kim, Younghun Kim, Younghee Kim, Sangku Lee

Abstract:

We investigated ecotoxicity and performed experiment for removing ZnO nanoparticles in water. Short term exposure of hatching test using fertilized eggs (O. latipes) showed deformity in 5ppm of ZnO nanoparticles solution. And in 10ppm ZnO nanoparticles solution delayed hatching was observed. Hereine, chemical precipitation method was suggested for removing ZnO nanoparticles in water. The precipitated ZnO nanoparticles showed the form of ZnS after addition of Na2S, and the form of Zn3(PO4)2 for Na2HPO4. The removal efficiency of ZnO nanoparticles in water was closed to 100% for two cases. In ecotoxicity evaluation of as-precipitated ZnS and Zn3(PO4)2, they did not cause any acute toxicity for D. magna. It is noted that this precipitation treatment of ZnO is effective to reduce the potential cytotoxicity.

Keywords: ZnO nanoparticles, ZnS, Zn3(PO4)2, ecotoxicity evaluation, chemical precipitation.

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1764 Modeling of Electrokinetic Mixing in Lab on Chip Microfluidic Devices

Authors: Virendra J. Majarikar, Harikrishnan N. Unni

Abstract:

This paper sets to demonstrate a modeling of electrokinetic mixing employing electroosmotic stationary and time-dependent microchannel using alternate zeta patches on the lower surface of the micromixer in a lab on chip microfluidic device. Electroosmotic flow is amplified using different 2D and 3D model designs with alternate and geometric zeta potential values such as 25, 50, and 100 mV, respectively, to achieve high concentration mixing in the electrokinetically-driven microfluidic system. The enhancement of electrokinetic mixing is studied using Finite Element Modeling, and simulation workflow is accomplished with defined integral steps. It can be observed that the presence of alternate zeta patches can help inducing microvortex flows inside the channel, which in turn can improve mixing efficiency. Fluid flow and concentration fields are simulated by solving Navier-Stokes equation (implying Helmholtz-Smoluchowski slip velocity boundary condition) and Convection-Diffusion equation. The effect of the magnitude of zeta potential, the number of alternate zeta patches, etc. are analysed thoroughly. 2D simulation reveals that there is a cumulative increase in concentration mixing, whereas 3D simulation differs slightly with low zeta potential as that of the 2D model within the T-shaped micromixer for concentration 1 mol/m3 and 0 mol/m3, respectively. Moreover, 2D model results were compared with those of 3D to indicate the importance of the 3D model in a microfluidic design process.

Keywords: COMSOL, electrokinetic, electroosmotic, microfluidics, zeta potential.

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1763 Periodic Orbits in a Delayed Nicholson's Blowflies Model

Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out.

Keywords: Nicholson's blowflies model, Stability, Hopf bifurcation, Delay.

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1762 Periodic Solutions for a Delayed Population Model on Time Scales

Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established.

Keywords: Coincidence degree, continuation theorem, periodic solutions, time scales

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1761 Effect of Addition Rate of Expansive Additive on Autogenous Shrinkage and Delayed Expansion of Ultra-High Strength Mortar

Authors: Yulu Zhang, Atushi Teramoto, Taka-Aki Ohkubo

Abstract:

In this study, the effect of expansive additives on autogenous shrinkage and delayed expansion of ultra-high strength mortar was explored. The specimens made for the study were composed of ultra-high strength mortar, which was mixed with ettringite-lime composite type expansive additive. Two series of experiments were conducted with the specimens. The experimental results confirmed that the autogenous shrinkage of specimens was effectively decreased by increasing the proportion of the expansive additive. On the other hand, for the specimens, which had 7% expansive additive, and were cured for seven days at a constant temperature of 20°C, and then cured for a long time in either in an underwater, moist (Relative humidity: 100%) or dry air (Relative humidity: 60%) environment, excessively large expansion strain occurred. Specifically, typical turtle shell-like swelling expansion cracks were confirmed in the specimens that underwent long-term curing in an underwater and moist environment. According to the result of hydration analysis, the formation of expansive substances, calcium hydroxide and alumina, ferric oxide, tri-sulfate contribute to the occurrence of delayed expansion.

Keywords: Ultra-high strength mortar, expansive additive, autogenous shrinkage, delayed expansion.

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1760 Hopf Bifurcation Analysis for a Delayed Predator–prey System with Stage Structure

Authors: Kejun Zhuang

Abstract:

In this paper, a delayed predator–prey system with stage structure is investigated. Sufficient conditions for the system to have multiple periodic solutions are obtained when the delay is sufficiently large by applying Bendixson-s criterion. Further, some numerical examples are given.

Keywords: Predator-prey system, Stage structure, Hopf bifurcation, Periodic solutions.

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1759 Pseudo-almost Periodic Solutions of a Class Delayed Chaotic Neural Networks

Authors: Farouk Cherif

Abstract:

This paper is concerned with the existence and unique¬ness of pseudo-almost periodic solutions to the chaotic delayed neural networks (t)= —Dx(t) ± A f (x (t)) B f (x (t — r)) C f (x(p))dp J (t) . t-o Under some suitable assumptions on A, B, C, D, J and f, the existence and uniqueness of a pseudo-almost periodic solution to equation above is obtained. The results of this paper are new and they complement previously known results.

Keywords: Chaotic neural network, Hamiltonian systems, Pseudo almost periodic.

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1758 Multiple Periodic Solutions for a Delayed Predator-prey System on Time Scales

Authors: Xiaoquan Ding, Jianmin Hao, Changwen Liu

Abstract:

This paper is devoted to a delayed periodic predatorprey system with non-monotonic numerical response on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of multiple periodic solutions. As corollaries, some applications are listed. In particular, our results improve and generalize some known ones.

Keywords: Predator-prey system, periodic solution, time scale, delay, coincidence degree.

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1757 Role of Biorefining and Biomass Utilization in Environmental Control

Authors: Subir Kundu, Sukhendra Singh, Sumedha Ojha, Kanika Kundu

Abstract:

The continuous decline of petroleum and natural gas reserves and non linear rise of oil price has brought about a realisation of the need for a change in our perpetual dependence on the fossil fuel. A day to day increased consumption of crude and petroleum products has made a considerable impact on our foreign exchange reserves. Hence, an alternate resource for the conversion of energy (both liquid and gas) is essential for the substitution of conventional fuels. Biomass is the alternate solution for the present scenario. Biomass can be converted into both liquid as well as gaseous fuels and other feedstocks for the industries.

Keywords: Bioenergy, Biomass conversion, Biorefining, Efficient utilisation of night soil.

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1756 Efficient Utilization of Biomass for Bioenergy in Environmental Control

Authors: Subir Kundu, Sukhendra Singh, Sumedha Ojha, Kanika Kundu

Abstract:

The continuous decline of petroleum and natural gas reserves and non linear rise of oil price has brought about a realisation of the need for a change in our perpetual dependence on the fossil fuel. A day to day increased consumption of crude and petroleum products has made a considerable impact on our foreign exchange reserves. Hence, an alternate resource for the conversion of energy (both liquid and gas) is essential for the substitution of conventional fuels. Biomass is the alternate solution for the present scenario. Biomass can be converted into both liquid as well as gaseous fuels and other feedstocks for the industries.

Keywords: Bioenergy, Biomass conversion, Biorefining, Efficient utilisation of night soil.

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1755 Enhancing Seismic Performance of Ductile Moment Frames with Delayed Wire-Rope Bracing Using Middle Steel Plate

Authors: Babak Dizangian, Mohammad Reza Ghasemi, Akram Ghalandari

Abstract:

Moment frames have considerable ductility against cyclic lateral loads and displacements; however, if this feature causes the relative displacement to exceed the permissible limit, it can impose unfavorable hysteretic behavior on the frame. Therefore, adding a bracing system with the capability of preserving the capacity of high energy absorption and controlling displacements without a considerable increase in the stiffness is quite important. This paper investigates the retrofitting of a single storey steel moment frame through a delayed wire-rope bracing system using a middle steel plate. In this model, the steel plate lies where the wire ropes meet, and the model geometry is such that the cables are continuously under tension so that they can take the most advantage of the inherent potential they have in tolerating tensile stress. Using the steel plate also reduces the system stiffness considerably compared to cross bracing systems and preserves the ductile frame’s energy absorption capacity. In this research, the software models of delayed wire-rope bracing system have been studied, validated, and compared with other researchers’ laboratory test results.

Keywords: Ductile moment frame, delayed wire rope bracing, cyclic loading, hysteresis curve, energy absorption.

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1754 A Bayesian Hierarchical 13COBT to Correct Estimates Associated with a Delayed Gastric Emptying

Authors: Leslie J.C.Bluck, Sarah J.Jackson, Georgios Vlasakakis, Adrian Mander

Abstract:

The use of a Bayesian Hierarchical Model (BHM) to interpret breath measurements obtained during a 13C Octanoic Breath Test (13COBT) is demonstrated. The statistical analysis was implemented using WinBUGS, a commercially available computer package for Bayesian inference. A hierarchical setting was adopted where poorly defined parameters associated with a delayed Gastric Emptying (GE) were able to "borrow" strength from global distributions. This is proved to be a sufficient tool to correct model's failures and data inconsistencies apparent in conventional analyses employing a Non-linear least squares technique (NLS). Direct comparison of two parameters describing gastric emptying ng ( tlag -lag phase, t1/ 2 -half emptying time) revealed a strong correlation between the two methods. Despite our large dataset ( n = 164 ), Bayesian modeling was fast and provided a successful fitting for all subjects. On the contrary, NLS failed to return acceptable estimates in cases where GE was delayed.

Keywords: Bayesian hierarchical analysis, 13COBT, Gastricemptying, WinBUGS.

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1753 Bifurcation Analysis of a Plankton Model with Discrete Delay

Authors: Anuj Kumar Sharma, Amit Sharma, Kulbhushan Agnihotri

Abstract:

In this paper, a delayed plankton-nutrient interaction model consisting of phytoplankton, zooplankton and dissolved nutrient is considered. It is assumed that some species of phytoplankton releases toxin (known as toxin producing phytoplankton (TPP)) which is harmful for zooplankton growth and this toxin releasing process follows a discrete time variation. Using delay as bifurcation parameter, the stability of interior equilibrium point is investigated and it is shown that time delay can destabilize the otherwise stable non-zero equilibrium state by inducing Hopf-bifurcation when it crosses a certain threshold value. Explicit results are derived for stability and direction of the bifurcating periodic solution by using normal form theory and center manifold arguments. Finally, outcomes of the system are validated through numerical simulations.

Keywords: Plankton, Time delay, Hopf-bifurcation, Normal form theory, Center manifold theorem.

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1752 Four Positive Almost Periodic Solutions to an Impulsive Delayed Plankton Allelopathy System with Multiple Exploit (or Harvesting) Terms

Authors: Fengshuo Zhang, Zhouhong Li

Abstract:

In this paper, we obtain sufficient conditions for the existence of at least four positive almost periodic solutions to an impulsive delayed periodic plankton allelopathy system with multiple exploited (or harvesting) terms. This result is obtained through the use of Mawhins continuation theorem of coincidence degree theory along with some properties relating to inequalities.

Keywords: Almost periodic solutions, plankton allelopathy system, coincidence degree, impulse.

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1751 Bifurcation Analysis in a Two-neuron System with Different Time Delays

Authors: Changjin Xu

Abstract:

In this paper, we consider a two-neuron system with time-delayed connections between neurons. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation results are given to support the theoretical predictions. Finally, main conclusions are given.

Keywords: Two-neuron system, delay, stability, Hopf bifurcation.

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1750 Positive Periodic Solutions in a Discrete Competitive System with the Effect of Toxic Substances

Authors: Changjin Xu, Qianhong Zhang

Abstract:

In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.

Keywords: Competitive system, periodic solution, discrete time delay, topological degree.

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1749 Frequency Domain Analysis for Hopf Bifurcation in a Delayed Competitive Web-site Model

Authors: Changjin Xu, Yusen Wu

Abstract:

In this paper, applying frequency domain approach, a delayed competitive web-site system is investigated. By choosing the parameter α as a bifurcation parameter, it is found that Hopf bifurcation occurs as the bifurcation parameter α passes a critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.

Keywords: Web-site system, stability, Nyquist criterion, Hopf bifurcation, frequency domain.

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1748 Observer Design for Chaos Synchronization of Time-delayed Power Systems

Authors: Jui-Sheng Lin, Yi-Sung Yang, Meei-Ling Hung, Teh-Lu Liao, Jun-Juh Yan

Abstract:

The global chaos synchronization for a class of time-delayed power systems is investigated via observer-based approach. By employing the concepts of quadratic stability theory and generalized system model, a new sufficient criterion for constructing an observer is deduced. In contrast to the previous works, this paper proposes a theoretical and systematic design procedure to realize chaos synchronization for master-slave power systems. Finally, an illustrative example is given to show the applicability of the obtained scheme.

Keywords: Chaos, Synchronization, Quadratic stability theory, Observer

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1747 Combined Effect of Heat Stimulation and Delayed Addition of Superplasticizer with Slag on Fresh and Hardened Property of Mortar

Authors: Faraidoon Rahmanzai, Mizuki Takigawa, Yu Bomura, Shigeyuki Date

Abstract:

To obtain the high quality and essential workability of mortar, different types of superplasticizers are used. The superplasticizers are the chemical admixture used in the mix to improve the fluidity of mortar. Many factors influenced the superplasticizer to disperse the cement particle in the mortar. Nature and amount of replaced cement by slag, mixing procedure, delayed addition time, and heat stimulation technique of superplasticizer cause the varied effect on the fluidity of the cementitious material. In this experiment, the superplasticizers were heated for 1 hour under 60 °C in a thermostatic chamber. Furthermore, the effect of delayed addition time of heat stimulated superplasticizers (SP) was also analyzed. This method was applied to two types of polycarboxylic acid based ether SP (precast type superplasticizer (SP2) and ready-mix type superplasticizer (SP1)) in combination with a partial replacement of normal Portland cement with blast furnace slag (BFS) with 30% w/c ratio. On the other hands, the fluidity, air content, fresh density, and compressive strength for 7 and 28 days were studied. The results indicate that the addition time and heat stimulation technique improved the flow and air content, decreased the density, and slightly decreased the compressive strength of mortar. Moreover, the slag improved the flow of mortar by increasing the amount of slag, and the effect of external temperature of SP on the flow of mortar was decreased. In comparison, the flow of mortar was improved on 5-minute delay for both kinds of SP, but SP1 has improved the flow in all conditions. Most importantly, the transition points in both types of SP appear to be the same, at about 5±1 min.  In addition, the optimum addition time of SP to mortar should be in this period.

Keywords: Combined effect, delayed addition, heat stimulation, flow of mortar.

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1746 Stability Analysis in a Fractional Order Delayed Predator-Prey Model

Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

Keywords: Fractional predator-prey model, laplace transform, characteristic equation.

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1745 Vehicle Aerodynamics: Drag Reduction by Surface Dimples

Authors: C. K. Chear, S. S. Dol

Abstract:

For a bluff body, dimples behave like roughness elements in stimulating a turbulent boundary layer, leading to delayed flow separation, a smaller wake and lower form drag. This is very different in principle from the application of dimples to streamlined body, where any reduction in drag would be predominantly due to a reduction in skin friction. In the present work, a car model with different dimple geometry is simulated using k-ε turbulence modeling to determine its effect to the aerodynamics performance. Overall, the results show that the application of dimples manages to reduce the drag coefficient of the car model.

Keywords: Aerodynamics, Boundary Layer, Dimple, Drag, Kinetic Energy, Turbulence.

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1744 The Influence of Mobile Phone's Forms in the User Perception

Authors: The Jaya Suteja, Stephany Tedjohartoko

Abstract:

Not all types of mobile phone are successful in entering the market because some types of the mobile phone have a negative perception of user. Therefore, it is important to understand the influence of mobile phone's characteristics in the local user perception. This research investigates the influence of QWERTY mobile phone's forms in the perception of Indonesian user. First, some alternatives of mobile phone-s form are developed based on a certain number of mobile phone's models. At the second stage, some word pairs as design attributes of the mobile phone are chosen to represent the user perception of mobile phone. At the final stage, a survey is conducted to investigate the influence of the developed form alternatives to the user perception. Based on the research, users perceive mobile phone's form with curved top and straight bottom shapes and mobile phone's form with slider and antenna as the most negative form. Meanwhile, mobile phone's form with curved top and bottom shapes and mobile phone-s form without slider and antenna are perceived by the user as the most positive form.

Keywords: Influence, mobile phone, form, user perception.

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1743 Limit Cycle Behaviour of a Neural Controller with Delayed Bang-Bang Feedback

Authors: Travis Wiens, Greg Schoenau, Rich Burton

Abstract:

It is well known that a linear dynamic system including a delay will exhibit limit cycle oscillations when a bang-bang sensor is used in the feedback loop of a PID controller. A similar behaviour occurs when a delayed feedback signal is used to train a neural network. This paper develops a method of predicting this behaviour by linearizing the system, which can be shown to behave in a manner similar to an integral controller. Using this procedure, it is possible to predict the characteristics of the neural network driven limit cycle to varying degrees of accuracy, depending on the information known about the system. An application is also presented: the intelligent control of a spark ignition engine.

Keywords: Control and automation, artificial neural networks, limit cycle

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1742 Multiple Positive Periodic Solutions of a Delayed Predatory-Prey System with Holling Type II Functional Response

Authors: Kaihong Zhao, Jiuqing Liu

Abstract:

In this letter, we considers a delayed predatory-prey system with Holling type II functional response. Under some sufficient conditions, the existence of multiple positive periodic solutions is obtained by using Mawhin’s continuation theorem of coincidence degree theory. An example is given to illustrate the effectiveness of our results.

Keywords: Multiple positive periodic solutions, Predatory-prey system, Coincidence degree, Holling type II functional response.

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