Dynamic Behaviors of a Discrete Periodic Predator-Prey-Mutualist System

A nonautonomous discrete predator-prey-mutualist system is proposed and studied in this paper. Sufficient conditions which ensure the permanence and existence of a unique globally stable periodic solution are obtained. We also investigate the extinction property of the predator species; our results indicate that if the cooperative effect between the prey and mutualist species is large enough, then the predator species will be driven to extinction due to the lack of enough food. Two examples together with numerical simulations show the feasibility of the main results

Nonlinear dynamics of plankton ecosystem with impulsive control and environmental fluctuations

It is well known that the density of plankton populations always increases and decreases or keeps invariant for a long time, and the variation of plankton density is an important factor influencing the real aquatic environments, why do these situations occur? It is an interesting topic which has become the common interest for many researchers. As the basis of the food webs in oceans, lakes, and reservoirs, plankton plays a significant role in the material circulation and energy flow for real aquatic ecosystems that have a great effect on the economic and social values. Planktonic blooms can occur in some environments, however, and the direct or indirect adverse effects of planktonic blooms on real aquatic ecosystems, such as water quality, water landscape, aquaculture development, are sometimes catastrophic, and thus planktonic blooms have become a challenging and intractable problem worldwide in recent years. Therefore, to understand these effects so that some necessary measures can be taken, it is important and meaningful to investigate the dynamic growth mechanism of plankton and reveal the dynamics mechanisms of formation and disappearance of planktonic blooms. To this end, based on the background of the ecological environments in the subtropical lakes and reservoirs, this dissertation research takes mainly the planktonic algae as the research objective to model the mechanisms of plankton growth and evolution. In this dissertation, some theories related to population dynamics, impulsive control dynamics, stochastic dynamics, as well as the methods of dynamic modeling, dynamic analysis and experimental simulation, are applied to reveal the effects of some key biological factors on the dynamics mechanisms of the spatial-temporal distribution of plankton and the termination of planktonic blooms, and to predict the dynamics evolutionary processes of plankton growth. The main results are as follows: Firstly, to discuss the prevention and control strategies on planktonic blooms, an impulsive reaction-diffusion hybrid system was developed. On the one hand, the dynamic analysis showed that impulsive control can significantly influence the dynamics of the system, including the ultimate boundedness, extinction, permanence, and the existence and uniqueness of positive periodic solution of the system. On the other hand, some experimental simulations were preformed to reveal that impulsive control can lead to the extinction and permanence of population directly. More precisely, the prey and intermediate predator populations can coexist at any time and location of their inhabited domain, while the top predator population undergoes extinction when the impulsive control parameter exceeds some a critical value, which can provide some key arguments to control population survival by means of some reaction-diffusion impulsive hybrid systems in the real life. Additionally, a heterogeneous environment can affect the spatial distribution of plankton and change the temporal-spatial oscillation of plankton distribution. All results are expected to be helpful in the study of dynamic complex of ecosystems. Secondly, a stochastic phytoplankton-zooplankton system with toxic phytoplankton was proposed and the effects of environmental stochasticity and toxin-producing phytoplankton (TPP) on the dynamics mechanisms of the termination of planktonic blooms were discussed. The research illustrated that white noise can aggravate the stochastic oscillation of plankton density and a high-level intensity of white noise can accelerate the extinction of plankton and may be advantageous for the disappearance of harmful phytoplankton, which imply that the white noise can help control the biomass of plankton and provide a guide for the termination of planktonic blooms. Additionally, some experimental simulations were carried out to reveal that the increasing toxin liberation rate released by TPP can increase the survival chance of phytoplankton population and reduce the biomass of zooplankton population, but the combined effects of those two toxin liberation rates on the changes in plankton are stronger than that of controlling any one of the two TPP. All results suggest that both white noise and TPP can play an important role in controlling planktonic blooms. Thirdly, we established a stochastic phytoplankton-toxic producing phytoplankton-zooplankton system under regime switching and investigated how the white noise, regime switching and TPP affect the dynamics mechanisms of planktonic blooms. The dynamical analysis indicated that both white noise and toxins released by TPP are disadvantageous to the development of plankton and may increase the risk of plankton extinction. Also, a series of experimental simulations were carried out to verify the correctness of the dynamical analysis and further reveal the effects of the white noise, regime switching and TPP on the dynamics mechanisms of the termination of planktonic blooms. On the one hand, the numerical study revealed that the system can switch from one state to another due to regime shift, and further indicated that the regime switching can balance the different survival states of plankton density and decrease the risk of plankton extinction when the density of white noise are particularly weak. On the other hand, an increase in the toxin liberation rate can increase the survival chance of phytoplankton but reduce the biomass of zooplankton, which implies that the presence of toxic phytoplankton may have a positive effect on the termination of planktonic blooms. These results may provide some insightful understanding on the dynamics of phytoplankton-zooplankton systems in randomly disturbed aquatic environments. Finally, a stochastic non-autonomous phytoplankton-zooplankton system involving TPP and impulsive perturbations was studied, where the white noise, impulsive perturbations and TPP are incorporated into the system to simulate the natural aquatic ecological phenomena. The dynamical analysis revealed some key threshold conditions that ensure the existence and uniqueness of a global positive solution, plankton extinction and persistence in the mean. In particular, we determined if there is a positive periodic solution for the system when the toxin liberation rate reaches a critical value. Some experimental simulations also revealed that both white noise and impulsive control parameter can directly influence the plankton extinction and persistence in the mean. Significantly, enhancing the toxin liberation rate released by TPP increases the possibility of phytoplankton survival but reduces the zooplankton biomass. All these results can improve our understanding of the dynamics of complex of aquatic ecosystems in a fluctuating environment

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Natural Selection Reconsidered

In this thesis, I inspect some key assumptions which tend to underpin mainstream accounts of natural selection, noting where those assumptions break down and taking this as a basis for fresh analysis. First, I examine the assumption that natural selection inherently involves struggle or competition. I show selection can take place without zero-sum competition and that competition is not essential for selection to positively facilitate novel adaptations. Moving on to fitness, I address the assumption that biological fitness should be measured as a function of the number of elements of some set of entities (offspring, gene copies or otherwise). Noting cases where selection seemingly acts in terms of persistence and somatic growth, and with these alternative fitness metrics not reducible to one another, I suggest a pluralist stance. Subsequently extending this rationale to the temporal dimension, I show that attempting to measure fitness over any single time frame often fails to capture the action of selection. In later chapters, I explore the possibility of uniting my multiple fitness metrics via a single “common currency” metric. I rule out metrics based around resource or energy consumption, as per Van Valen and others, as unworkable. However, I find some potential in conceptualising the various aspects of fitness in terms of negative entropy. This fails to deliver a quantifiable common currency metric, but does address conceptual issues and allows for the unification of our account of biological fitness with the popular thermodynamic definition of life. The need to buttress earlier arguments necessitates a concluding analysis of the Darwinian population concept. Contra complacent assumptions that they are readily defined, I find that there are no clear means to bound Darwinian populations in many cases. I also argue that analysis of the Darwinian population concept has been confounded by the conflation of pragmatic groupings, assembled for comparative inference, with causally bound Darwinian populations

Partial Differential Equations in Ecology

Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots

Holistic biomimicry: a biologically inspired approach to environmentally benign engineering

Humanity's activities increasingly threaten Earth's richness of life, of which mankind is a part. As part of the response, the environmentally conscious attempt to engineer products, processes and systems that interact harmoniously with the living world. Current environmental design guidance draws upon a wealth of experiences with the products of engineering that damaged humanity's environment. Efforts to create such guidelines inductively attempt to tease right action from examination of past mistakes. Unfortunately, avoidance of past errors cannot guarantee environmentally sustainable designs in the future. One needs to examine and understand an example of an environmentally sustainable, complex, multi-scale system to engineer designs with similar characteristics. This dissertation benchmarks and evaluates the efficacy of guidance from one such environmentally sustainable system resting at humanity's doorstep - the biosphere. Taking a holistic view of biomimicry, emulation of and inspiration by life, this work extracts overarching principles of life from academic life science literature using a sociological technique known as constant comparative method. It translates these principles into bio-inspired sustainable engineering guidelines. During this process, it identifies physically rooted measures and metrics that link guidelines to engineering applications. Qualitative validation for principles and guidelines takes the form of review by biology experts and comparison with existing environmentally benign design and manufacturing guidelines. Three select bio-inspired guidelines at three different organizational scales of engineering interest are quantitatively validated. Physical experiments with self-cleaning surfaces quantify the potential environmental benefits generated by applying the first, sub-product scale guideline. An interpretation of a metabolically rooted guideline applied at the product / organism organizational scale is shown to correlate with existing environmental metrics and predict a sustainability threshold. Finally, design of a carpet recycling network illustrates the quantitative environmental benefits one reaps by applying the third, multi-facility scale bio-inspired sustainability guideline. Taken as a whole, this work contributes (1) a set of biologically inspired sustainability principles for engineering, (2) a translation of these principles into measures applicable to design, (3) examples demonstrating a new, holistic form of biomimicry and (4) a deductive, novel approach to environmentally benign engineering. Life, the collection of processes that tamed and maintained themselves on planet Earth's once hostile surface, long ago confronted and solved the fundamental problems facing all organisms. Through this work, it is hoped that humanity has taken one small step toward self-mastery, thus drawing closer to a solution to the latest problem facing all organisms.Ph.D.Committee Chair: Bert Bras; Committee Member: David Rosen; Committee Member: Dayna Baumeister; Committee Member: Janet Allen; Committee Member: Jeannette Yen; Committee Member: Matthew Realf

Population Dynamics and Pattern Formation in an Info-chemical Mediated Tri-trophic Plankton Model

In this thesis, we study a spatio–temporal prey–predator model of plankton. This model has spatial interaction terms which represent a plankton dynamics that includes info–chemical mediated trophic interactions. We consider both a simplified two species model which has been studied in the literature (mostly in biological terms) and an extended, four-species model. In the latter, the grazing pressure of microzooplankton (M) on phytoplankton (P) is controlled through external infochemical (C) mediated predation by copepods (Z). We undertake a stability analysis of both the two species model and the four species model and compare the system dynamics. In relation to this, the critical conditions for Turing instability are derived; these are necessary and sufficient. Furthermore, we consider the degenerated situation wherein Turing bifurcation and Hopf bifurcation occur simultaneously. We also consider under what conditions Turing patterns are exhibited and under what conditions spatiotemporal patterns are observed generally. The Transient Turing instability of spatial interactions –exhibited by the two species model–is introduced and investigated in a number of ways. We also study the effects of the paradox of enrichment. This paradox led to a loss of stability in the four species model after this was derived from the two species model by expansion and by the addition of resources. Further, a numerical continuation technique was used to determine the existence of multiple stationary patterns

Dynamical Models of Biology and Medicine

Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicin