Discrete Lotka-Volterra systems in one dimension (the logistic equation) and two dimensions have been studied extensively, revealing a wealth of complex dynamical regimes. We show that three-dimensional discrete Lotka...Discrete Lotka-Volterra systems in one dimension (the logistic equation) and two dimensions have been studied extensively, revealing a wealth of complex dynamical regimes. We show that three-dimensional discrete Lotka-Volterra dynamical systems exhibit all of the dynamics of the lower dimensional systems and a great deal more. In fact and in particular, there are dynamical features including analogs of flip bifurcations, Neimark-Sacker bifurcations and chaotic strange attracting sets that are essentially three-dimensional. Among these are new generalizations of Neimark-Sacker bifurcations and novel chaotic strange attractors with distinctive candy cane type shapes. Several of these dynamical are investigated in detail using both analytical and simulation techniques.展开更多
Ecological variables play a significant role in determining the diversity and distribution of any living organism on earth. Lichens are not exceptional and are quite sensitive in comparison to other organisms; hence t...Ecological variables play a significant role in determining the diversity and distribution of any living organism on earth. Lichens are not exceptional and are quite sensitive in comparison to other organisms; hence the present study focuses on the impact of ecological variables on the diversity and distribution of epiphytic macrolichens colonizing Quercus leucotrichophora across eight different sites(50 m × 50 m) in Thal Ke Dhar forest, Kumaun Himalaya, Uttarakhand, India. For sampling of macrolichens, 200 trees(25 trees from each site) of Q.leucotrichophora were selected from each site and five quadrats of 5 cm × 10 cm(1000 quadrats in totality) were drawn at the tree trunk. From all the sampled trees, a total of 54 species of epiphytic macrolichens belonging to 18 genera and five families were recorded. Various ecological variables, namely altitude, aspect, slope, diameter at breast height(DBH), and lopping percent(partial cutting of the twigs as disturbance), were also analyzed to investigate their influence on macrolichen species composition and distribution pattern in the study area. For the determination of relationships between these variables, statistical analysis, namely Pearson's Correlation Coefficient, Polynomial regression analysis and Principal Component Analysis(PCA)were performed. Out of all variables, lopping was significantly correlated to species richness of epiphytic macrolichens(0.712~*, p<0.05) and it was confirmed by Pearson's Correlation Coefficient.Despite of having high anthropogenic pressure or impact through lopping, the maximum number of macrolichen species was recorded at elevation 2267 meter above sea level(m asl). The present study revealed that besides other ecological variables,lopping practices can act as a key parameter incontrolling the diversity and distribution not only of epiphytic macrolichens but also of other life forms such as bryophytes, pteridophytes, insects, birds etc.and can be either negatively or positively correlated.展开更多
文摘Discrete Lotka-Volterra systems in one dimension (the logistic equation) and two dimensions have been studied extensively, revealing a wealth of complex dynamical regimes. We show that three-dimensional discrete Lotka-Volterra dynamical systems exhibit all of the dynamics of the lower dimensional systems and a great deal more. In fact and in particular, there are dynamical features including analogs of flip bifurcations, Neimark-Sacker bifurcations and chaotic strange attracting sets that are essentially three-dimensional. Among these are new generalizations of Neimark-Sacker bifurcations and novel chaotic strange attractors with distinctive candy cane type shapes. Several of these dynamical are investigated in detail using both analytical and simulation techniques.
基金Head, Department of Botany, S.S.J. Campus Kumaun University, Almora - 263601 for providing laboratory facilities and G. B. Pant National Institute of Himalayan Environment and Sustainable Development, Kosi-Katarmal, Almora263643 (GBPI/IERP/16-17/16/175) for financial assistance
文摘Ecological variables play a significant role in determining the diversity and distribution of any living organism on earth. Lichens are not exceptional and are quite sensitive in comparison to other organisms; hence the present study focuses on the impact of ecological variables on the diversity and distribution of epiphytic macrolichens colonizing Quercus leucotrichophora across eight different sites(50 m × 50 m) in Thal Ke Dhar forest, Kumaun Himalaya, Uttarakhand, India. For sampling of macrolichens, 200 trees(25 trees from each site) of Q.leucotrichophora were selected from each site and five quadrats of 5 cm × 10 cm(1000 quadrats in totality) were drawn at the tree trunk. From all the sampled trees, a total of 54 species of epiphytic macrolichens belonging to 18 genera and five families were recorded. Various ecological variables, namely altitude, aspect, slope, diameter at breast height(DBH), and lopping percent(partial cutting of the twigs as disturbance), were also analyzed to investigate their influence on macrolichen species composition and distribution pattern in the study area. For the determination of relationships between these variables, statistical analysis, namely Pearson's Correlation Coefficient, Polynomial regression analysis and Principal Component Analysis(PCA)were performed. Out of all variables, lopping was significantly correlated to species richness of epiphytic macrolichens(0.712~*, p<0.05) and it was confirmed by Pearson's Correlation Coefficient.Despite of having high anthropogenic pressure or impact through lopping, the maximum number of macrolichen species was recorded at elevation 2267 meter above sea level(m asl). The present study revealed that besides other ecological variables,lopping practices can act as a key parameter incontrolling the diversity and distribution not only of epiphytic macrolichens but also of other life forms such as bryophytes, pteridophytes, insects, birds etc.and can be either negatively or positively correlated.