Volterra Model Research Articles

DYNAMICS OF MODIFIED LOTKA–VOLTERRA MODEL WITH POLYNOMIAL INTERVENTION FACTORS. METHODOLOGICAL ASPECTS. III

In the present article is considered a modification of the classicalLotka–Volterra model. The ’input functions alpha(t) and gamma(t) are algebraic polynomi-als of degree n, alpha(t) is monotonically increasing (with ”saturation”) and gamma(t) > 0 ismonotonically decreasing in the considered interval. This model is very sensitive withrespect to the coefficients of the polynomials ai and bi. Therefore it is attractive forconducting computer simulations, including other modified predator-prey models andactivator-inhibitor mechanisms. Numerical examples, illustrating our results are givenusing CAS Mathematica.

Modeling the temporal dynamics of gut microbiota from a local community perspective

Given gut microbiota's important role in human health, a clear understanding of the microbial ecosystem dynamics is vital. Mathematical models for analyzing time-series data of gut microbiotas would, therefore, be highly beneficial. Although a generalized Lotka–Volterra (gLV) model for identifying the interactions between gut microbiota members and quantifying the effects of external factors already exists, it is limited in its practical applications. Therefore, we established a stochastic gLV model for analyzing temporal data about the gut microbiota from a local community perspective and provided a reliable parameter estimation method for our model. Our model has abilities similar to those of the existing gLV model but can also capture emigration/immigration effects and avoid the existing model's inadequacies. To test our model's applicability, we fitted our model on a previously published data set. We found the interactions between the gut microbiota of different individuals and between different periods for the same individual were different in the data sets. Analysis of the random dynamic characteristics of the gut microbiota revealed that the number of microorganisms in the local community tended to decrease as a result of random factors, but the numbers were restored by the immigration of external microbes .

An Improved Lotka–Volterra Model Using Quantum Game Theory

Human decision-making does not conform to the independent decision-making hypothesis from classical decision-making theory. Thus, we introduce quantum decision-making theory into the Lotka–Volterra model (L–V model), to investigate player population dynamics while incorporating the initial strategy, game payoffs and interactive strategies in an open social system. Simulation results show that: (1) initial strategy, entanglement intensity of strategy interaction, and payoffs impact population dynamics; (2) In cooperative coexistence, game players mutually exceed the initial environmental capacity in an open system, but not in competitive coexistence; (3) In competitive coexistence, an initial strategy containing an entanglement intensity of strategies plays a vital role in game outcomes. Furthermore, our proposed model more realistically delineates the characteristics of population dynamics in competitive or cooperative coexistence scenarios.

Antagonistic effects of long- and short-term environmental variation on species coexistence.

Assessing the impact of environmental fluctuations on species coexistence is critical for understanding biodiversity loss and the ecological impacts of climate change. Yet determining how properties like the intensity, frequency or duration of environmental fluctuations influence species coexistence remains challenging, presumably because previous studies have focused on indefinite coexistence. Here, we model the impact of environmental fluctuations at different temporal scales on species coexistence over a finite time period by employing the concepts of time-windowed averaging and performance curves to incorporate temporal niche differences within a stochastic Lotka-Volterra model. We discover that short- and long-term environmental variability has contrasting effects on transient species coexistence, such that short-term variation favours species coexistence, whereas long-term variation promotes competitive exclusion. This dichotomy occurs because small samples (e.g. environmental changes over long time periods) are more likely to show large deviations from the expected mean and are more difficult to predict than large samples (e.g. environmental changes over short time periods), as described in the central limit theorem. Consequently, we show that the complex set of relationships among environmental fluctuations and species coexistence found in previous studies can all be synthesized within a general framework by explicitly considering both long- and short-term environmental variation.

A Bivariate Volterra Series Model for the Design of Power Amplifier Digital Predistorters.

The operation of the power amplifier (PA) in wireless transmitters presents a trade-off between linearity and power efficiency, being more efficient when the device exhibits the highest nonlinearity. Its modeling and linearization performance depend on the quality of the underlying Volterra models that are characterized by the presence of relevant terms amongst the enormous amount of regressors that these models generate. The presence of PA mechanisms that generate an internal state variable motivates the adoption of a bivariate Volterra series perspective with the aim of enhancing modeling capabilities through the inclussion of beneficial terms. In this paper, the conventional Volterra-based models are enhanced by the addition of terms, including cross products of the input signal and the new internal variable. The bivariate versions of the general full Volterra (FV) model and one of its pruned versions, referred to as the circuit-knowledge based Volterra (CKV) model, are derived by considering the signal envelope as the internal variable and applying the proposed methodology to the univariate models. A comparative assessment of the bivariate models versus their conventional counterparts is experimentally performed for the modeling of two PAs driven by a 30 MHz 5G New Radio signal: a class AB PA and a class J PA. The results for the digital predistortion of the class AB PA under a direct learning architecture reveal the benefits in linearization performance produced by the bivariate CKV model structure compared to that of the univariate CKV model.

Plenty accurate soliton wave solutions of the prototype of an excitable system

In this paper, the nonlinear fractional Lotka–Volterra model is analyzed and numerically studied. This research is based on applying the three latest analytical schemes and three other numerical schemes to construct rich wave solutions. In different forms, many novel solitary wave solutions are built and presented in two-dimensional, three-dimensional, and contour plots. The numerical method conditions are evaluated through the obtained analytical solutions, and the accuracy of the analytical solutions is studied. Many numerical solutions are constructed based on the employed schemes. Additionally, the analytical, semi-analytical, numerical, and absolute values of error between the values of obtained solutions are calculated with the different values of the given variable in the solutions. Furthermore, the match between the obtained analytical solution and the numerical solution has been explained through some two-dimensional distributed radar charts. The contribution of this article is demonstrated by comparing the obtained solution with the recently published results of the same model.

Towards a New Continuous Improvement Organization Based on Simulation

The paper proposes a mathematical model to forecast the time needed during a continuous improvement (CI) project. To do this, the authors adapted the famous Lotka–Volterra model to the CI methodology. Also, the authors examined a Montreal company’s database to simulate the CI’s necessary time in the real world. Firstly, the model simulates a total of CI hours for the employees and the respective quantity of problems at the end of the project. And after, the authors compared the simulation results with the project real results. This work introduces a new model to forecast the CI’s necessary time and discuss an innovative way to implement a CI project. This work also considers the advantages and difficulties of achieving a CI project based on a simulation. One of the work’s main result is the discussion of the total CI hours performed by the employees: 130% of the simulation proposition. This quantity of hours leads to half of the problems estimated by the model: 42%. The normalized results showed a difference of 1.03% between the simulation and the observations in the real world.

Co-evolution of Construction Waste Recycling Industrial Chain Based on Lotka–volterra Model

Under the green building policy, the recycling of construction waste has become an important issue. However, many obstructions in the industrial chain of construction waste recycling, slow integration of production elements in the chain, and inefficient resource allocation hinder the development of the construction waste recycling industry. In this study, a co-evolution model of the industrial chain of construction waste recycling is constructed based on the Lotka–Volterra model, and the Jacobian matrix is used for stability analysis. Finally, a numerical simulation is performed. The simulation results indicate that: (1) There is a high product correlation between upstream and downstream enterprises in the industrial chain of construction waste recycling; (2) The conversion coefficient of supply and demand of upstream and downstream enterprises has a higher impact on and is more sensitive to the evolution of this industrial chain; (3) The co-evolution of upstream and downstream enterprises promotes the added value of products and maximizes the overall benefits of the industrial chain, which provides reference value and theoretical basis for the development of the industrial chain of construction waste recycling.

Cross-target transfer algorithm based on the volterra model of SSVEP-BCI

In general, a large amount of training data can effectively improve the classification performance of the Steady-State Visually Evoked Potential (SSVEP)-based Brain-Computer Interface (BCI) system. However, it will prolong the training time and considerably restrict the practicality of the system. This study proposed a SSVEP nonlinear signal model based on the Volterra filter, which could reconstruct stable reference signals using relatively small number of training targets by transfer learning, thereby reducing the training cost of SSVEP-BCI. Moreover, this study designed a transfer-extended Canonical Correlation Analysis (t-eCCA) method based on the model to achieve cross-target transfer. As a result, in a single-target SSVEP experiment with 16 stimulus frequencies, t-eCCA obtained an average accuracy of 86.96%±12.87% across 12 subjects using only half of the calibration time, which exhibited no significant difference from the representative training classification algorithms, namely, extended canonical correlation analysis (88.32%±13.97%) and task-related component analysis (88.92%±14.44%), and was significantly higher than that of the classic non-training algorithms, namely, Canonical Correlation Analysis (CCA) as well as filter-bank CCA. Results showed that the proposed cross-target transfer algorithm t-eCCA could fully utilize the information about the targets and its stimulus frequencies and effectively reduce the training time of SSVEP-BCI.

Incentive strategy about technology innovation based on knowledge ecological coupling in strategic emerging industry

PurposeThe purpose of this paper is to solve the problem of low efficiency on knowledge resources allocation in the strategic emerging industry (SEI), an incentive model of technology innovation based on knowledge ecological coupling is designed.Design/methodology/approachFirst, a principal–agent model of knowledge inputs and a knowledge ecological coupling model based on an improved Lotka–Volterra model are constructed. In addition, a numerical example about Chongqing Yongchuan industrial park, the emulation analysis and the associated discussions are conducted to analyze the equilibriums of principal–agent in different knowledge inputs. Further, the paper analyzes the evolutionary equilibrium in knowledge ecological coupling and reveals the dual adjustments of the node organization on knowledge inputs.FindingsThus, this paper shows that by establishing the relationships of knowledge ecological coupling based on “mutualism and commensalism,” node organization raises the level of knowledge inputs; an incentive mode of “knowledge ecological coupling relationship + technology innovation chain” is conductive to substantially improving the efficiency of knowledge resource allocation, and to stimulate the vitality of node organization for technology innovation in the strategic emerging industry (SEI).Originality/valueThis paper contributes to the extant researches in two ways. First, this paper reveals the dual adjustments of the node organizations in inputting knowledge, which broadens the vision and borders of the researches on traditional knowledge management. The methods of the traditional principal–agent model and the knowledge input/output profit model are also expanded. Second, this paper verifies that applying the mode of “knowledge ecological coupling relationship + technology innovation chain” in practice is conducive to enhancing the efficiency of the cross-organizational knowledge allocation in the strategic emerging industry (SEI).

Competition Analysis on Industry Populations Based on a Three-Dimensional Lotka–Volterra Model

The classical Lotka–Volterra model is mainly a two-dimensional configuration. The two-dimensional form limits the application scenarios of the Lotka–Volterra model. The research objective of this paper is to develop a feasible three population equilibrium model to analyze the industry competition. In order to expand the Lotka–Volterra model to empirical analysis, this paper proposes a symbiosis model of enterprise population based on a three-dimensional Lotka–Volterra model. This paper analyzes the symbiotic system from two aspects: the balanced development of three species and the competitive evolution of the three species, taking the sales volume of three local automobile enterprises in China as the sample for empirical analysis. The symbiotic optimization under the equilibrium state of three populations indicates that there is the possibility of equilibrium and reciprocity in the growth of three automobile product populations. The empirical analysis fully explains the feasibility of this research paradigm. The analysis of competition evolution shows that cooperative action is better than competitive strategy and that comprehensive cooperation is the ideal state of a three-population symbiotic system.

Stable Coexistence in a Field-Calibrated Individual-Based Model of Mangrove Forest Dynamics Caused by Inter-Specific Crown Plasticity

(1,2) In this theoretical study, we apply MesoFON, a field-calibrated individual-based model of mangrove forest dynamics, and its Lotka–Volterra interpretations to address two questions: (a) Do the dynamics of two identical red mangrove species that compete for light resources and avoid inter-specific competition by lateral crown displacement follow the predictions of classical competition theory or resource competition theory? (b) Which mechanisms drive the dynamics in the presence of inter-specific crown plasticity when local competition is combined with global or with localized seed dispersal? (3) In qualitative support of classical competition theory, the two species can stably coexist within MesoFON. However, the total standing stock at equilibrium matched the carrying capacity of the single species. Therefore, a “non-overyielding” Lotka–Volterra model rather than the classic one approximated best the observed behavior. Mechanistically, inter-specific crown plasticity moved heterospecific trees apart and pushed conspecifics together. Despite local competition, the community exhibited mean-field dynamics with global dispersal. In comparison, localized dispersal slowed down the dynamics by diminishing the strength of intra-/inter-specific competition and their difference due to a restriction in the competitive race to the mean-field that prevails between conspecific clusters. (4) As the outcome in field-calibrated IBMs is mediated by the competition for resources, we conclude that classical competition mechanisms can override those of resource competition, and more species are likely to successfully coexist within communities.

Parameter Estimation of the Lotka–Volterra Model with Fractional Order Based on the Modulation Function and Its Application

The Lotka–Volterra model is widely applied in various fields, and parameter estimation is important in its application. In this study, the Lotka–Volterra model with universal applicability is established by introducing the fractional order. Modulation function is multiplied by both sides of the Lotka–Volterra model, and the model is converted into linear equations with parameters to be estimated by the fractional integration method. The parameters are obtained by solving the equations. The state of the system is estimated by shifted Chebyshev polynomial. Last, the implementation program of the model is compiled. The concrete implementation method of the improved model is proposed by an example in this study.

An efficient identification approach for highly complex non-linear systems using the evolutionary computing method based Kalman filter

This paper proposes a new and efficient approach where a nature-inspired optimisation technique has abetted the Kalman filter (KF) for accurately solving the parametric estimation problem of highly complex non-linear systems. The KF is the best optimal state estimator in terms of normalised mean squared error (NMSE) for linear Gaussian state-space models. However, the use of mismatched noise statistics in KF might result in performance degradation. To address this issue, three steps are proposed in this work for the accurate estimation of the unknown non-linear system parameters by using the Volterra model. The first step is to reformulate the Volterra model into a measurement form. Secondly, the KF parameters are optimised by using an evolutionary algorithm with an efficient objective function. The third step is to estimate the coefficients of the unknown system by using the KF technique with the help of optimally tuned KF parameters achieved in the second step. In simulations, three distinct higher memory size second-order Volterra models, two non-linear benchmark systems and the primary path of active-noise control (ANC) system based on real data sets are identified by using the basic KF, genetic algorithm (GA) assisted KF (GA-KF), particle swarm optimisation (PSO) assisted KF (PSO-KF), firefly algorithm (FA) assisted KF (FA-KF) and ant lion optimisation (ALO) assisted KF (ALO-KF) techniques. The experimental results illustrate that the ALO-KF approach leads to better coefficient estimation compared to FA-KF, PSO-KF, GA-KF, and basic KF methods.

MODEL OF INTERACTIONS AND PHASE STATES IN THE DISTRIBUTION OF THE FREQUENCY RESOURCE IN THE GROUPING OF RADIO ELECTRONIC MEANS OF A 5G MOBILE COMMUNICATION NETWORK

Subject: interaction models and phase states in the distribution of the frequency resource in the grouping of radio electronic means of the 5G mobile communication network. Purpose: development of a dynamic model of multiple interactions of n-elements of a complex 5G mobile communication system, which takes into account the nature of inter-element connections and phase states in the group use of the frequency resource. Tasks: on the basis of a complex model of an n-element system with multiple interactions, to develop a mathematical model for describing the electromagnetic environment of a grouping of radio electronic means in a state space with a group use of a frequency resource; to analyze the phase states of interaction of the elements of the grouping system of radio-electronic means of the mobile communication system in which they can function without deteriorating the quality indicators, which reflect the total level of the group influence of the emitting elements on the receiving devices, under conditions of optimal distribution of the frequency resource. Methods: mathematical method of the state space of the system, which describes the nonlinear nature and phase states of the system, taking into account the intensity of the interaction of its elements. Results: A mathematical model of the electromagnetic environment of a grouping of radio-electronic devices based on the Volterra model has been developed, which characterizes their nonlinear nature of interactions in the group use of the frequency resource. A recurrent expression is obtained for modeling the assessment of the aggregate nature of electromagnetic interactions in a group of radio-electronic means. Modeling of the dynamics of interaction and phase states of the grouping of radioelectronic devices in the group use of the frequency resource has been carried out. Conclusions: It is shown that using a model that simulates the dynamics of interactions of a group of radioelectronic, it is possible to analyze its state in the future. This model makes it possible to analyze the grouping of radio-electronic means with different, specific parameters of individual types of radio electronic devices, the nature and intensity of their interaction in the grouping with the current distribution of resources.

Nonlinear Dynamics Identification of the Oculo-Motor System based on Eye Tracking Data

Instrumental computing and software tools have been developed for constructing a nonlinear dynamic model of the human oculo-motor system (OMS) based on the data of input–output experiments using test visual stimuli and innovative technology eye tracking. For identification the Volterra model is used in the form of multidimensional transient functions of the 1st, 2nd and 3rd orders, taking into account the inertial and nonlinear properties of the OMS. Software tools for processing eye tracking data developed in the Matlab environment are tested on real data from an experimental study of OMS.

Structural identifiability of the generalized Lotka-Volterra model for microbiome studies.

Population dynamic models can be used in conjunction with time series of species abundances to infer interactions. Understanding microbial interactions is a prerequisite for numerous goals in microbiome research, including predicting how populations change over time, determining how manipulations of microbiomes affect dynamics and designing synthetic microbiomes to perform tasks. As such, there is great interest in adapting population dynamic theory for microbial systems. Despite the appeal, numerous hurdles exist. One hurdle is that the data commonly obtained from DNA sequencing yield estimates of relative abundances, while population dynamic models such as the generalized Lotka–Volterra model track absolute abundances or densities. It is not clear whether relative abundance data alone can be used to infer parameters of population dynamic models such as the Lotka–Volterra model. We used structural identifiability analyses to determine the extent to which a time series of relative abundances can be used to parametrize the generalized Lotka–Volterra model. We found that only with absolute abundance data to accompany relative abundance estimates from sequencing can all parameters be uniquely identified. However, relative abundance data alone do contain information on relative interaction strengths, which is sufficient for many studies where the goal is to estimate key interactions and their effects on dynamics. Using synthetic data of a simple community for which we know the underlying structure, local practical identifiability analysis showed that modest amounts of both process and measurement error do not fundamentally affect these identifiability properties.

Adaptive Genetic Algorithm Renewed by Migration Operator

In the present study, the Genetic Algorithm and the developed Adaptive Genetic Algorithm are used to solve optimization problems faced in modeling of complex systems. While using the Genetic Algorithm and the Adaptive Genetic Algorithm, the most important problem encountered is that these algorithms are prone to getting stuck in local bests. For example, in the complex system data optimization process using the Genetic Algorithm, it has been observed that it is frequently fitted to local bests in a certain period of time. The reasons are that, many mutations cannot be performed in the limited number of iterations, and because the number of individuals is limited, the population is filled with the same set of solutions in a short time. Therefore, the migration operator has been added to the Genetic Algorithm and the Adaptive Genetic algorithm in order to avoid local bests and to provide that these algorithms search in a wider area of the large search space of complex systems. In the present study, we have tested these algorithms using the migration operator in the Lotka Volterra Model. When the results are examined, it is observed that the Adaptive Genetic Algorithm with migration operator outperforms the Genetic Algorithm and the targeted success is achieved in complex system optimization. In the rest of the paper, the algorithms used in the Method Section are explained with outlines. In the Experimental Studies Section, the different algorithms are tested and compared with each other in the Lotka-Voltera model and numerical test functions. In the Conclusions and Discussions Section, brief information is given about general results and future studies.

Multiobjective Evaluation of Coevolution among Innovation Populations Based on Lotka–Volterra Equilibrium

The collaborative evaluation of enterprise innovation populations is a hot issue. The Lotka–Volterra model is a mature method used to evaluate the interaction mechanism of populations and is widely used in innovation ecology research studies. The Lotka–Volterra model mainly focuses on the quantitative characteristics of the interactive populations. The growth mechanisms cannot explain all the synergy mechanisms of the innovative populations. The collaborative evaluation between enterprise innovation populations is a typical multiobjective evaluation problem. The multichoice goal programming model is a mature method to solve multiobjective optimization problems. This paper combines the Lotka–Volterra model and multichoice goal programming method to construct a three-stage multiobjective collaboration evaluation method based on Lotka–Volterra equilibrium. An evaluation example is used to illustrate the application process of this method. The method proposed in this paper has excellent performance in computing, parameter sensitivity analysis, and model stability analysis.

RETRACTED ARTICLE: Coopetition analysis in industry upgrade and urban expansion based on fractional derivative gray Lotka–Volterra model

RETRACTED ARTICLE: Coopetition analysis in industry upgrade and urban expansion based on fractional derivative gray Lotka–Volterra model