• Title, Summary, Keyword: Lotka-Volterra systems

### On the Dynamics of Multi-Dimensional Lotka-Volterra Equations

• Abe, Jun;Matsuoka, Taiju;Kunimatsu, Noboru
• 제어로봇시스템학회:학술대회논문집
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• pp.1623-1628
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• 2004
• In the 3-dimensional cyclic Lotka-Volterra equations, we show the solution on the invariant hyperplane. In addition, we show the existence of the invariant hyperplane by the center manifold theorem under the some conditions. With this result, we can lead the hyperplane of the n-dimensional cyclic Lotka-Volterra equaions. In other section, we study the 3- or 4-dimensional Hamiltonian Lotka-Volterra equations which satisfy the Jacobi identity. We analyze the solution of the Hamiltonian Lotka- Volterra equations with the functions called the split Liapunov functions by [4], [5] since they provide the Liapunov functions for each region separated by the invariant hyperplane. In the cyclic Lotka-Volterra equations, the role of the Liapunov functions is the same in the odd and even dimension. However, in the Hamiltonian Lotka-Volterra equations, we can show the difference of the role of the Liapunov function between the odd and the even dimension by the numerical calculation. In this paper, we regard the invariant hyperplane as the important item to analyze the motion of Lotka-Volterra equations and occur the chaotic orbit. Furtheremore, an example of the asymptoticaly stable and stable solution of the 3-dimensional cyclic Lotka-Volterra equations, 3- and 4-dimensional Hamiltonian equations are shown.

### Coexistence in competitive Lotka-volterra systems

• Kim, Jung-Gi
• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.147-151
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• 1996
• In this paper we consider n-species autonomous competitive Lotka-Volterra systems. We exhibit here simple algebraic criteria on the parameters which guarantee the coexistence of all the species.

### Multi-group Competitive Dynamics Modeling and Analysis between Major Automakers in Korean Automobile Market (한국 자동차 시장 내 주요 기업간 다집단 경쟁 다이나믹스 모델링 및 분석)

• Song, Young Han;Kim, Young;Jung, Gisun;Kim, Yun Bae
• Journal of the Korea Society for Simulation
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• v.29 no.4
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• pp.55-64
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• 2020
• Since the European Union-South Korea Free Trade Agreement entered into force in 2011, the Korean automobile market has grown rapidly, resulting in intensifying competition among companies in the market. European automakers gained price competitiveness, which intensified competition with Korean automakers. In such a situation, various studies on the Korean automobile market have been conducted, but studies such as market influencing factor analysis and consumer analysis have mainly been conducted, and there is no research on the analysis of competitive dynamics in the market. In this study, the competitive dynamics between Hyundai Motors, Kia Motors, Mercedes-Benz, and BMW, which are major automakers in the Korean automobile market, are analyzed. The competitive relationship between major automakers are modeled using the Lotka-Volterra (LV) model and the competitive dynamics over time are analyzed by applying the Moving Window. In order to explain the competitive dynamics effectively, we analyze it by subdividing it based on various influencing factors.

### Forecasting Model of Container Transshipment Traffic Volume in Northeast Asia (동북아시아 환적물동량 예측모델 연구)

• Lee, Byoung-Chul;Kim, Yun-Bae
• Journal of Korean Institute of Industrial Engineers
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• v.37 no.4
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• pp.297-303
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• 2011
• Major ports in Northeastern Asia engage in fierce competition to attract transshipment traffic volume. Existing time series analyses for analyzing port competition relationships examine the types of competition and relations through the signs of coefficients in cointegration equations using the transshipment traffic volume results. However, there are cases for which analyzing competing relationships is not possible based on the results of the transshipment traffic volume data differences and limitations in the forecasting of traffic volume. Accordingly, we used the Lotka-Volterra (L-V) model,also known as the ecosystem competitive relation model, to analyze port competition relations for the long-term forecast of South Korean transshipment traffic volume.

### Permanence of a Three-species Food Chain System with Impulsive Perturbations

• Baek, Hunki;Lee, Hung-Hwan
• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.503-514
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• 2008
• We investigate a three-species food chain system with Lotka-Volterra functional response and impulsive perturbations. In [23], Zhang and Chen have studied the system. They have given conditions for extinction of lowest-level prey and top predator and considered the local stability of lower-level prey and top predator eradication periodic solution. However, they did not give a condition for permanence, which is one of important facts in population dynamics. In this paper, we establish the condition for permanence of the three-species food chain system with impulsive perturbations. In addition, we give some numerical examples.

### Almost Periodic Processes in Ecological Systems with Impulsive Perturbations

• Stamov, Gani Trendafilov
• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.299-312
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• 2009
• In the present paper we investigate the existence of almost periodic processes of ecological systems which are presented with nonautonomous N-dimensional impulsive Lotka Volterra competitive systems with dispersions and fixed moments of impulsive perturbations. By using the techniques of piecewise continuous Lyapunov's functions new sufficient conditions for the global exponential stability of the unique almost periodic solutions of these systems are given.

### Simulation Analysis of Multi-group Competitive Relationships between Platforms in Social Network Service (SNS) Market (SNS 시장 내 플랫폼 간 다집단 경쟁관계 시뮬레이션 분석)

• Choi, Jong You;Jung, Gisun;Kim, Young;Kim, Yun Bae
• Journal of the Korea Society for Simulation
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• v.29 no.4
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• pp.9-19
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• 2020
• The number of customers on Social Network Services(SNS) is rapidly increasing with the spread of smartphones. As of 2018, about 2.7 billion people of the world population (about 7.1 billion people) and more than 31.2 million people of the total population of South Korea (about 50.1 million) use SNS. There are several studies have been conducted on increasing SNS market. Most of them, however, were not quantitative but qualitative studies. This study is conducted on domestic SNS market to identify the competitive relationship among SNS platforms with great proportion in South Korea, such as Facebook, Instagram and Twitter. The objective is to suggest some hypotheses of the competitive relations, test them, and finally verify the trend of domestic SNS market. Competitive Lotka-Volterra (LV) model is used to find out the competitive relationships and Moving Window is also used to show the changes of them over time. In order to test the hypotheses on the relationships, some experiments are performed with Moving Window technique. Thus, the relations among the platforms and the changes of them over time are identified.

### STABILITY ANALYSIS FOR PREDATOR-PREY SYSTEMS

• Shim, Seong-A
• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.211-229
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• 2010
• Various types of predator-prey systems are studied in terms of the stabilities of their steady-states. Necessary conditions for the existences of non-negative constant steady-states for those systems are obtained. The linearized stabilities of the non-negative constant steady-states for the predator-prey system with monotone response functions are analyzed. The predator-prey system with non-monotone response functions are also investigated for the linearized stabilities of the positive constant steady-states.

### A dynamic competition among 3 fields & 17 key growth drivers of Korea (3대 분야 17개 신성장 동력 기술간 동태적 경쟁관계 분석)

• Kim, Moon-Soo;Lee, Sung-Joo
• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.5
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• pp.2067-2077
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• 2011
• The recent trend in technology development is characterized as technology convergence, mainly between IT, BT and NT and also more and more industries are starting to use several technologies simultaneously or in a combined way theses days. As a result, the needs on technology interaction analysis is increasing for strategic technology management and policy-making. Responding to the needs, this research deals with technology innovation process in terms of technology competition, particularly focusing on the 17 new growth drivers in 3 areas, which has been announced by the Korean government as a new growth vision for Korean economy, and analyzing their co-evolutionary process. For the analysis, patent data, a representative data on technology innovation, is adopted. Then, Lotka-Volterra Competition model, a model frequently used to describe the dynamism of competitive innovation is applied to the data. The research results are expected to support strategic decision-makings such as effect policy-making or R&D priority-setting, by analyzing the relationship between the 3 areas, the 17 new growth drivers, or the particular technologies in the drivers.

### Mathematical models for population changes of two interacting species (상호작용하는 두 생물 종의 개체 수 변화에 대한 수학적 모델)

• Shim, Seong-A
• Journal for History of Mathematics
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• v.25 no.1
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• pp.45-56
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• 2012
• Mathematical biology has been recognized its importance recently and widely studied in the fields of mathematics, biology, medical sciences, and immunology. Mathematical ecology is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats. It was the earliest form of the research field of mathematical biology and has been providing its basis. This article deals with various form of interactions between two biological species in a common habitat. Mathematical models of predator-prey type, competitive type, and simbiotic type are investigated.