A fractional B-spline collocation method for the numerical solution of fractional predator-prey models

We present a collocation method based on fractional B-splines for the solution of fractional differential problems. The key-idea is to use the space generated by the fractional B-splines, i.e., piecewise polynomials of noninteger degree, as approximating space. Then, in the collocation step the fractional derivative of the approximating function is approximated accurately and efficiently by an exact differentiation rule that involves the generalized finite difference operator. To show the effectiveness of the method for the solution of nonlinear dynamical systems of fractional order, we solved the fractional Lotka-Volterra model and a fractional predator-pray model with variable coefficients. The numerical tests show that the method we proposed is accurate while keeping a low computational cost

Plant structural complexity and mechanical defenses mediate predator-prey interactions in an odonate-bird system.

Habitat-forming species provide refuges for a variety of associating species; these refuges may mediate interactions between species differently depending on the functional traits of the habitat-forming species. We investigated refuge provisioning by plants with different functional traits for dragonfly and damselfly (Odonata: Anisoptera and Zygoptera) nymphs emerging from water bodies to molt into their adult stage. During this period, nymphs experience high levels of predation by birds. On the shores of a small pond, plants with mechanical defenses (e.g., thorns and prickles) and high structural complexity had higher abundances of odonate exuviae than nearby plants which lacked mechanical defenses and exhibited low structural complexity. To disentangle the relative effects of these two potentially important functional traits on nymph emergence-site preference and survival, we conducted two fully crossed factorial field experiments using artificial plants. Nymphs showed a strong preference for artificial plants with high structural complexity and to a lesser extent, mechanical defenses. Both functional traits increased nymph survival but through different mechanisms. We suggest that future investigations attempt to experimentally separate the elements contributing to structural complexity to elucidate the mechanistic underpinnings of refuge provisioning

Entropy and Fractal Techniques for Monitoring Fish Behaviour and Welfare in Aquacultural Precision Fish Farming—A Review

In a non-linear system, such as a biological system, the change of the output (e.g., behaviour) is not proportional to the change of the input (e.g., exposure to stressors). In addition, biological systems also change over time, i.e., they are dynamic. Non-linear dynamical analyses of biological systems have revealed hidden structures and patterns of behaviour that are not discernible by classical methods. Entropy analyses can quantify their degree of predictability and the directionality of individual interactions, while fractal dimension (FD) analyses can expose patterns of behaviour within apparently random ones. The incorporation of these techniques into the architecture of precision fish farming (PFF) and intelligent aquaculture (IA) is becoming increasingly necessary to understand and predict the evolution of the status of farmed fish. This review summarizes recent works on the application of entropy and FD techniques to selected individual and collective fish behaviours influenced by the number of fish, tagging, pain, preying/feed search, fear/anxiety (and its modulation) and positive emotional contagion (the social contagion of positive emotions). Furthermore, it presents an investigation of collective and individual interactions in shoals, an exposure of the dynamics of inter-individual relationships and hierarchies, and the identification of individuals in groups. While most of the works have been carried out using model species, we believe that they have clear applications in PFF. The review ends by describing some of the major challenges in the field, two of which are, unsurprisingly, the acquisition of high-quality, reliable raw data and the construction of large, reliable databases of non-linear behavioural data for different species and farming conditions.The work was supported by the Spanish MINECO (Grant RTC-2014–2837-2- “SELATUN: Minimización de la problemática del mercurio del atún y valorización del atún como alimento saludable, Programa Retos-Colaboración 2014”. The funding source had no involvement in the preparation of this manuscript

Variational Embedded Solitons, And Traveling Wavetrains Generated By Generalized Hopf Bifurcations, In Some Nlpde Systems

In this Ph.D. thesis, we study regular and embedded solitons and generalized and degenerate Hopf bifurcations. These two areas of work are seperate and independent from each other. First, variational methods are employed to generate families of both regular and embedded solitary wave solutions for a generalized Pochhammer PDE and a generalized microstructure PDE that are currently of great interest. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the family of the trial functions). Thus, the residual is calculated, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that only the parameter regimes for the existence of solitary waves had previously been analyzed for the microstructure PDE considered here, the results obtained here are both new and timely

Complexity Study and Chaos Control in a Prey-Predator System

A prey-predator system has been investigated with the application of random shock. Since the fluctuations of populations are random, the applied shock is also assumed like a random noise. To study complexities during evolution, numerical simulations have been carried out for both cases, without shock and with shock. Stabilities of fixed points have been discussed for both the cases. Also, bifurcation diagrams for both the cases have been drawn by varying a parameter while keeping other parameters fixed. Numerical calculations have been extended to obtain plots of Lyapunov exponents and topological entropies as the measure of complexity in the system. It has been observed that the random shock has little impact to reduce the chaotic motion in the system. Then, certain periodic changes in a parameter have been allowed to some extent,this results in bringing the system from chaos to regularity. Such changes may happen naturally in a prey-predator system and so there exists the possibility of coexistence. The chaos indicator DLI has been used for clarity in detection of regular and chaotic motion. Finally,the correlation dimension for the chaotic set has also been calculated for certain set of parameter values

Modeling and control of complex dynamic systems: Applied mathematical aspects

The concept of complex dynamic systems arises in many varieties, including the areas of energy generation, storage and distribution, ecosystems, gene regulation and health delivery, safety and security systems, telecommunications, transportation networks, and the rapidly emerging research topics seeking to understand and analyse. Such systems are often concurrent and distributed, because they have to react to various kinds of events, signals, and conditions. They may be characterized by a system with uncertainties, time delays, stochastic perturbations, hybrid dynamics, distributed dynamics, chaotic dynamics, and a large number of algebraic loops. This special issue provides a platform for researchers to report their recent results on various mathematical methods and techniques for modelling and control of complex dynamic systems and identifying critical issues and challenges for future investigation in this field. This special issue amazingly attracted one-hundred-and eighteen submissions, and twenty-eight of them are selected through a rigorous review procedure

Trivial movements and redistribution of polyphagous insect herbivores in heterogeneous vegetation

The aim of this thesis was to study the interplay between movement patterns of polyphagous insect herbivores and vegetation heterogeneity within agricultural fields. I examined if and how 1) host plant species, 2) host plant quality, 3) vegetation architecture, and 4) trap crop physical design influence movement patterns of individuals and spatial distribution of populations. Foragers may aggregate in profitable areas by tactic movement, or by area-restricted search, i.e. by moving randomly but slowing down movement and increasing rate of turning after encountering a profitable patch. Movement patterns of polyphagous herbivores have a high potential for influencing their distribution among hosts differing in quality. However, information on the role random vs. non-random components in their movement behavior is scarce. The results of this thesis show that both host plant species and within species differences in host plant quality affect movement behavior of a polyphagous herbivore, the European tarnished plant bug nymphs. The host plant induced movement patterns also explained the distribution of nymphs in heterogeneous vegetation. Because redistribution was very fast, it appears that no tactic behavior is needed for the nymphs to locate preferred hosts in heterogeneous vegetation composed of small patches. Instead the nymphs may successfully locate superior hosts merely by random movement coupled with sensitivity to local host quality. The physical structure of environment influences redistribution of populations at several spatial scales. At small scale the architecture of vegetation may influence redistribution of insects that move on the plant surface. At large scale e.g. trap crop physical design may affect redistribution of pests. In this thesis I derive a model for predicting the impact of vegetation architecture on the rate of displacement by insects moving on the plant surface. I also present and explore models of the interplay between pest movement and trap crop physical design. The trap crop models suggest that considerable reduction in pest density may be achieved using small trap crop cover with trap crops that the pest distinctly prefers over the crop. It supports also the idea that trap crop placement may have a dramatic impact on the efficiency of the trap crops

Simulation modelling and visualisation: toolkits for building artificial worlds

Simulations users at all levels make heavy use of compute resources to drive computational simulations for greatly varying applications areas of research using different simulation paradigms. Simulations are implemented in many software forms, ranging from highly standardised and general models that run in proprietary software packages to ad hoc hand-crafted simulations codes for very specific applications. Visualisation of the workings or results of a simulation is another highly valuable capability for simulation developers and practitioners. There are many different software libraries and methods available for creating a visualisation layer for simulations, and it is often a difficult and time-consuming process to assemble a toolkit of these libraries and other resources that best suits a particular simulation model. We present here a break-down of the main simulation paradigms, and discuss differing toolkits and approaches that different researchers have taken to tackle coupled simulation and visualisation in each paradigm