STABILITY ANALYSIS OF A NONHOMOGENEOUS MARKOVIAN LANDSCAPE MODEL

被引：32

作者：

LI, BL

机构：

[1] Center for Biosystems Modelling, Department of Industrial Engineering, Texas A and M University, College Station

来源：

ECOLOGICAL MODELLING | 1995年 / 82卷 / 03期

基金：

美国国家科学基金会;

关键词：

LANDSCAPE DYNAMICS; MARKOV MODELS; SPATIAL PATTERNS; VEGETATION DYNAMICS;

D O I：

10.1016/0304-3800(94)00091-U

中图分类号：

Q14 [生态学（生物生态学）];

学科分类号：

071012 ; 0713 ;

摘要：

Quantitative methods to analyze spatial patterns of landscapes are an important area of research in landscape ecology. Nonhomogeneous Markov models can be used to represent landscape dynamics; however, methods to analyze the stability of these models are needed. A method for determining the stability is developed in this paper, and its application to a model of vegetation dynamics in southern Texas savanna is also given. Using Lyapunov stability theory, the theorem that the family of these transition matrices will be stable if the symmetric matrices associated with the vertex matrices have matrix measures less than two has been proved. The results of the stability analysis accord well with current understanding of vegetation dynamics in the southern Texas landscape.

引用

页码：247 / 256

页数：10

共 43 条

[1] HAVE SOUTHERN TEXAS SAVANNAS BEEN CONVERTED TO WOODLANDS IN RECENT HISTORY [J].

ARCHER, S .

AMERICAN NATURALIST, 1989, 134 (04) :545-561

[2] AUTOGENIC SUCCESSION IN A SUB-TROPICAL SAVANNA - CONVERSION OF GRASSLAND TO THORN WOODLAND [J].

ARCHER, S ;

SCIFRES, C ;

BASSHAM, CR ;

MAGGIO, R .

ECOLOGICAL MONOGRAPHS, 1988, 58 (02) :111-127

[3]

BAKER W L, 1989, Landscape Ecology, V2, P111, DOI 10.1007/BF00137155

[4] LANDSCAPE ECOLOGY AND NATURE RESERVE DESIGN IN THE BOUNDARY WATERS CANOE AREA, MINNESOTA [J].

BAKER, WL .

ECOLOGY, 1989, 70 (01) :23-35

[5]

BOTKIN DB, 1974, ECOSYSTEM ANAL PREDI, P144

[6] INVASION RESISTANCE ARISES IN STRONGLY INTERACTING SPECIES-RICH MODEL COMPETITION COMMUNITIES [J].

CASE, TJ .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1990, 87 (24) :9610-9614

[7]

Caswell H., 1991, Ecological Studies, P97

[8] DISTURBANCE, INTERSPECIFIC INTERACTION AND DIVERSITY IN METAPOPULATIONS [J].

CASWELL, H ;

COHEN, JE .

BIOLOGICAL JOURNAL OF THE LINNEAN SOCIETY, 1991, 42 (1-2) :193-218

[9]

Cinlar E, 2013, INTRO STOCHASTIC PRO

[10] DISPERSAL IN PATCHY ENVIRONMENTS - THE EFFECTS OF TEMPORAL AND SPATIAL STRUCTURE [J].

COHEN, D ;

LEVIN, SA .

THEORETICAL POPULATION BIOLOGY, 1991, 39 (01) :63-99

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