Effects of intraspecific cooperative interactions in large ecosystems

We analyze the role of the Allee effect - a positive correlation between population density and mean individual fitness - for ecological communities formed by a large number of species. Our study is performed using the generalized Lotka-Volterra model with random interactions between species. We obtain the phase diagram and analyze the nature of the multiple equilibria phase. Remarkable differences emerge with respect to the logistic growth case, thus revealing the major role played by the functional response in determining aggregate behaviors of large ecosystems.

Lotka-Volterra Model of Wastewater Treatment in Bioreactor System using 4th Order Runge-Kutta Method

Wastewater treatment is essential to preserve the ecosystem and to ensure water resources are uncontaminated. This paper presents the Lotka-Volterra model of nonlinear ordinary differential equations of the interaction between predator-prey and substrate. The dimensionless ordinary differential equations of the model are solved using the 4th Order Runge-Kutta method (RK4) in MATLAB®. This study discusses the behaviour parameters of predators, prey and substrate. The results are shown graphically for different values of each parameter. Hence, the biological reaction of clean water from the interaction of predator-prey and substrate in wastewater treatment is identified. The higher the concentration of prey, the faster the concentration of substrate reaches 0 with and without the natural death of prey. The clean water will be produced whenever the concentration of prey and the concentration of predator are in balance regardless of the natural death rate. Stability analysis using the Jacobian matrix at the equilibrium point is also performed to determine the stability of the system.

Interpretation and Dynamics of the Lotka–Volterra Model in the Description of a Three-Level Laser

In this work, the Lotka–Volterra equations where applied to laser physics to describe population inversion and the number of emitted photons. Given that predation and stimulated emissions are analogous processes, two rate equations where obtained by finding suitable parameter transformations for a three-level laser. This resulted in a set of differential equations which are isomorphic to several laser models under accurate parameter identification. Furthermore, the steady state provided two critical points: one where light amplification stops and another where continuous-wave operation is achieved. Lyapunov’s first method of stability yielded the conditions for the convergence to the continuous-wave point, whereas a Lyapunov potential provided its stability regions. Finally, the Q-Switching technique was modeled by introducing a periodic variation of the quality Q of the cavity. This resulted in the transformation of the asymptotically stable fixed point into a limit cycle in the phase space.

Building a classifier in the personality recognition system based on eye tracking data

Identification systems that use biometric characteristics to solve the problem of access to information systems are becoming more common. The article proposes a new method of biometric identification of computer systems users, based on the determination of the integral Volterra model of the human oculo-motor system (OMS) according to experimental research "input-output" using innovative eye tracking technology. With the help of the Tobii Pro TX300 eye tracker, the data of OMC responses to test visual stimuli were obtained, displayed as bright dots on the computer screen at different distances from the start position in the "horizontal" direction. Based on the data obtained, the transition functions of the first, second and third orders of the OMS for two people were determined. To construct a personality classifier, the informativeness of the proposed heuristic features, determined on the basis of the transition functions in terms of the probability of correct recognition (PCR), is investigated. Pairs of features are established that are resistant to computational errors and have a high PCR value - in the range 0.92 - 0.97. Fig.: 8. Table: 5. Bibliography: 30 items. Key words: biometric identification, personality recognition, Volterra model, oculo-motor system, eye tracking technology, informativeness of features, classification.

Competition Equilibrium Analysis of China’s Luxury Car Market Based on Three-Dimensional Grey Lotka–Volterra Model

An enterprise must be able to conduct in-depth analysis of the existing data as the information has certain grey characteristics, if it wants to occupy a dominant position in the fierce market competition. In this paper, a compound three-dimensional grey Lotka–Volterra model is developed to carry out the grey transformation of the original data, so that the data can have better simulation accuracy, and the observation noise of the original data can be reduced. The competitive situation analysis based on the three-dimensional grey Lotka–Volterra model can help enterprises better understand the market situation. This paper takes the luxury brand automobile market in mainland China as an example to conduct a competitive analysis and a balanced development simulation. It can be found that, based on Three Species System Analysis, there is a symbiotic relationship among automobile enterprises and that the three species model can be adopted in analyzing the competition and cooperation among enterprises. Through balanced development of a Symbiotic System Analysis, the results of symbiotic optimization under the achievable equilibrium state of three populations are obtained and they show that the proposed method can be used effectively to conduct the market competition analysis. It is thus of great importance to study the relationships among enterprises as it is helpful for enterprises to make strategic policies.

The Evaluation of Synergy between University Entrepreneurship Education Ecosystem and University Students’ Entrepreneurship Performance

The interactive mechanism between college and university entrepreneurship education ecosystem and their students’ entrepreneurial performance needs to be further discussed, as college and university students are an important force in entrepreneurship. Since there is a lack of symbiotic mechanism analysis and interactive optimization research using ecological methods, this paper constructs the evaluation index system of entrepreneurship education ecosystem and entrepreneurship performance evaluation index system and uses the entropy weight method to determine the weight of various indicators in the index system more objectively. In this paper, Lotka–Volterra model in ecology is used to deeply study the mechanism between college and university entrepreneurship education ecosystem and entrepreneurship performance. Lotka–Volterra multichoice goal programming (MCGP) model is used to optimize the collaborative relationship between college and university entrepreneurship education ecosystem and entrepreneurship performance. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the research method. The results show that Lotka–Volterra multichoice goal programming (MCGP) method is effective in evaluating the synergy between college and university entrepreneurship education ecosystem and the students’ entrepreneurship performance.

The Role of Energy Return on Energy Invested (EROEI) in Complex Adaptive Systems

The energy return on energy invested, EROI or EROEI, is the ratio of the energy produced by a system to the energy expended to build, maintain, and finally dismantle the system. It is an important parameter for evaluating the efficiency of energy-producing technologies. In this paper, we examine the concept of EROEI from the general viewpoint of dynamic dissipative systems, providing insights on a wider range of applications. In general, natural resources can be assimilated to energy stocks characterized by a potential that can be exploited by creating intermediate stocks. This transformation is typical of dissipative systems and for the first time, we report that the Lotka–Volterra model, usually confined to the study of the biology of populations, can represent a powerful tool to estimate the EROEI of dissipative systems and, in particular, those systems subjected to depletion. This assessment is important to evaluate the ongoing energy transition since it provides us with a model for the decline of the EROEI in the exploitation of fossil fuels.

Ratio-Dependence in Predator-Prey Systems as an Edge and Basic Minimal Model of Predator Interference

The functional response (trophic function or individual ration) quantifies the average amount of prey consumed per unit of time by a single predator. Since the seminal Lotka-Volterra model, it is a key element of the predation theory. Holling has enhanced the theory by classifying prey-dependent functional responses into three types that long remained a generally accepted basis of modeling predator-prey interactions. However, contradictions between the observed dynamics of natural ecosystems and the properties of predator-prey models with Holling-type trophic functions, such as the paradox of enrichment, the paradox of biological control, and the paradoxical enrichment response mediated by trophic cascades, required further improvement of the theory. This led to the idea of the inclusion of predator interference into the trophic function. Various functional responses depending on both prey and predator densities have been suggested and compared in their performance to fit observed data. At the end of the 1980s, Arditi and Ginzburg stimulated a lively debate having a strong impact on predation theory. They proposed the concept of a spectrum of predator-dependent trophic functions, with two opposite edges being the prey-dependent and the ratio-dependent cases, and they suggested revising the theory by using the ratio-dependent edge of the spectrum as a null model of predator interference. Ratio-dependence offers the simplest way of accounting for mutual interference in predator-prey models, resolving the abovementioned contradictions between theory and natural observations. Depending on the practical needs and the availability of observations, the more detailed models can be built on this theoretical basis.

Timescale Analyses of Fluctuations in Coexisting Populations of a Native and Invasive Tree Squirrel

1. Competition from invasive species is an increasing threat to biodiversity. In Southern California, the western gray squirrel (Sciurus griseus, WGS) is facing increasing competition from the fox squirrel (Sciurus niger, FS), an invasive congener. 2. We used spectral methods to analyze 140 consecutive monthly censuses of WGS and FS within a 11.3 ha section of the California Botanic Garden. Variation in the numbers for both species and their synchrony was distributed across long timescales (> 15 months). 3. After filtering out annual changes, concurrent mean monthly temperatures from nearby Ontario Airport (ONT) yielded a spectrum with a large semiannual peak and significant spectral power at long timescales (> 30 months). Squirrel-temperature cospectra showed significant negative covariation at long timescales (> 35 months) for WGS and smaller significant negative peaks at 6 months for both species. 4. Simulations from a Lotka-Volterra model of two competing species indicates that the risk of extinction for the weaker competitor increases quickly as environmental noise shifts from short to long timescales. 5. We analyzed the timescales of fluctuations in detrended mean annual temperatures for the time period 1915-2014 from 1218 locations across the continental USA. In the last two decades, significant shifts from short timescales to long timescales have occurred, changing from less than 3 years to 4-6 years. 6. Our results indicate that (i) population fluctuations in co-occurring native and invasive tree squirrels are synchronous, occur over long timescales, and may be driven by fluctuations in environmental conditions; (ii) long timescale population fluctuations increase the risk of extinction in competing species, especially for the inferior competitor; and (iii) the timescales of interannual environmental fluctuations may be increasing from recent historical values. These results have broad implications for the impact of climate change on the maintenance of biodiversity.