Chaotic Dynamics in a Three Species Aquatic Population Model with Holling Type II Functional Response

A three-trophic model for marine community is proposed and investigated by means of numerical bifurcation analysis. The proposed model based on a modified version of the Leslie-Gower scheme, incorporates mutual interference in all the three populations and generalizes several other known models in the ecological literature. We investigate the dynamical behavior of the model system by considering the Holling type II functional response of toxin liberation process. Bifurcation diagram and two-dimensional parameter scan suggest that chaotic dynamics is robust to variations in toxin production by phytoplankton. Our study suggests that toxic substances released by TPP population may act as bio-control by changing the state of chaos to order. The mutual interference also induces chaos and acts as both stabilizing and destabilizing factors

Persistence and Extinction of One-Prey and Two-Predators System

In this paper, a mathematical model is proposed and analysed to study the dynamics of one-prey two-predators system with ratio-dependent predators growth rate. Criteria for local stability, instability and global stability of the nonnegative equilibria are obtained. The permanent co-existence of the three species is also discussed. Finally, computer simulations are performed to investigate the dynamics of the system

Chaos to order: role of toxin producing phytoplankton in aquatic system

Toxin producing phytoplankton (TPP) plays an important role in aquatic systems. To observe the role of TPP, we consider a three species food chain model consisting of TPP-zooplankton-fish population. The similar type of model considered by Upadhyay et al. [1] for terrestrial ecosystem and obtained chaotic dynamics in some region of parametric space. We modify their models by taking into account the toxin liberation process of TPP population and represented as aquatic systems. We consider Holling type I, type II and type III functional forms for this process. We observe that increasing the strength of toxic substance change the state from chaos to order. Our conclusion is that TPP has a stabilizing contribution in aquatic systems and may be used as a bio-control mechanism

Chaos to Order: Role of Toxin Producing Phytoplankton in Aquatic Systems

Toxin producing phytoplankton (TPP) plays an important role in aquatic systems. To observe the role of TPP, we consider a three species food chain model consisting of TPP-zooplankton-fish population. The similar type of model considered by Upadhyay et al. [1] for terrestrial ecosystem and obtained chaotic dynamics in some region of parametric space. We modify their models by taking into account the toxin liberation process of TPP population and represented as aquatic systems. We consider Holling type I, type II and type III functional forms for this process. We observe that increasing the strength of toxic substance change the state from chaos to order. Our conclusion is that TPP has a stabilizing contribution in aquatic systems and may be used as a bio-control mechanism

Dynamical Complexity in Some Ecological Models: Effects of Toxin Production by Phytoplankton

We investigate dynamical complexities in two types of chaotic tri-trophic aquatic food-chain model systems representing a real situation in the marine environment. Phytoplankton produce chemical substances known as toxins to reduce grazing pressure by zooplankton [1]. The role of toxin producing phytoplankton (TPP) on the chaotic behavior in these food chain systems is investigated. Holling type I, II, and III functional response forms are considered to study the interference between phytoplankton and zooplankton populations in the presence of toxic chemical. Our study shows that chaotic dynamics is robust to changes in the rates of toxin release as well as the toxin release functions. The present study also reveals that the rate of toxin production by toxin producing phytoplankton plays an important role in controlling oscillations in the plankton system. The different mortality functions of zooplankton due to toxin producing phytoplankton have significant influence in controlling oscillations, coexistence, survival or extinction of the zooplankton population. Further studies are needed to ascertain if this defence mechanism suppresses chaotic dynamics in model aquatic systems

Refractometric Determination of Formation Constants of Au(III), Pt(IV), Os(VIII) & Ir(III) Complexes

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Wide field CCD photometry of the young open cluster NGC 663

A deep and wide field CCD photometry of the young open cluster NGC 663 has been carried out. We report preliminary results of our investigations, specifically the determination of the cluster mass function which is found variable within the cluster region

Dynamics of Phytoplankton, Zooplankton and Fishery Resource Model

In this paper, a new mathematical model has been proposed and analyzed to study the interaction of phytoplankton- zooplankton-fish population in an aquatic environment with Holloing’s types II, III and IV functional responses. It is assumed that the growth rate of phytoplankton depends upon the constant level of nutrient and the fish population is harvested according to CPUE (catch per unit effort) hypothesis. Biological and bionomical equilibrium of the system has been investigated. Using Pontryagin’s Maximum Principal, the optimal harvesting policy is discussed. Chaotic nature and bifurcation analysis of the model system for a control parameter have been observed through a numerical simulation

Relating Gribov-Zwanziger theory to effective Yang-Mills theory

We consider the Gribov-Zwanziger (GZ) theory with appropriate horizon term which exhibits the nilpotent BRST invariance. This infinitesimal BRST transformation has been generalized by allowing the parameter to be finite and field dependent (FFBRST). By constructing appropriate finite field dependent parameter we show that the generating functional of GZ theory with horizon term is related to that of Yang-Mills (YM) theory through FFBRST transformation.Comment: 14 pages, No figure, to appear in Europhysics Lette