The qualitative behavior of solutions for a generalized Gause type predator prey system was studied.A large number of biological and bioeconomic models are special cases of this system.The system was investigated in t...The qualitative behavior of solutions for a generalized Gause type predator prey system was studied.A large number of biological and bioeconomic models are special cases of this system.The system was investigated in the region D={(x,y)|x>0,y>0} because of the biological meaning of the system.The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system,which ensure that the system has at least one limit cycle.The theory of limit sets of autonomous plane systems and the theorem of cycle field of Poincare Bendixson are efficiently employed in the research.The main results and their consequences presented not only generalize some known results,but also improve some corresponding results of other authors.展开更多
In this work,we study a predator-prey model of Gause type,in which the prey growth rate is subject to an Allee effect and the action of the predator over the prey is determined by a generalized hyperbolic-type functio...In this work,we study a predator-prey model of Gause type,in which the prey growth rate is subject to an Allee effect and the action of the predator over the prey is determined by a generalized hyperbolic-type functional response,which is neither differentiable nor locally Lipschitz at the predator axis.This kind of functional response is an extension of the so-called square root functional response,used to model systems in which the prey have a strong herd structure.We study the behavior of the solutions in the first quadrant and the existence of limit cycles.We prove that,for a wide choice of parameters,the solutions arrive at the predator axis in finite time.We also characterize the existence of an equilibrium point and,when it exists,we provide necessary and sufficient conditions for it to be a center-type equilibrium.In fact,we show that the set of parameters that yield a center-type equilibrium,is the graph of a function with an open domain.We also prove that any center-type equilibrium is stable and it always possesses a supercritical Hopf bifurcation.In particular,we guarantee the existence of a unique limit cycle,for small perturbations of the system.展开更多
The analysis of microstates in EEG signals is a crucial technique for understanding the spatiotemporal dynamics of brain electrical activity.Traditional methods such as Atomic Agglomerative Hierarchical Clustering(AAH...The analysis of microstates in EEG signals is a crucial technique for understanding the spatiotemporal dynamics of brain electrical activity.Traditional methods such as Atomic Agglomerative Hierarchical Clustering(AAHC),K-means clustering,Principal Component Analysis(PCA),and Independent Component Analysis(ICA)are limited by a fixed number of microstate maps and insufficient capability in cross-task feature extraction.Tackling these limitations,this study introduces a Global Map Dissimilarity(GMD)-driven density canopy K-means clustering algorithm.This innovative approach autonomously determines the optimal number of EEG microstate topographies and employs Gaussian kernel density estimation alongside the GMD index for dynamic modeling of EEG data.Utilizing this advanced algorithm,the study analyzes the Motor Imagery(MI)dataset from the GigaScience database,GigaDB.The findings reveal six distinct microstates during actual right-hand movement and five microstates across other task conditions,with microstate C showing superior performance in all task states.During imagined movement,microstate A was significantly enhanced.Comparison with existing algorithms indicates a significant improvement in clustering performance by the refined method,with an average Calinski-Harabasz Index(CHI)of 35517.29 and a Davis-Bouldin Index(DBI)average of 2.57.Furthermore,an information-theoretical analysis of the microstate sequences suggests that imagined movement exhibits higher complexity and disorder than actual movement.By utilizing the extracted microstate sequence parameters as features,the improved algorithm achieved a classification accuracy of 98.41%in EEG signal categorization for motor imagery.A performance of 78.183%accuracy was achieved in a four-class motor imagery task on the BCI-IV-2a dataset.These results demonstrate the potential of the advanced algorithm in microstate analysis,offering a more effective tool for a deeper understanding of the spatiotemporal features of EEG signals.展开更多
文摘The qualitative behavior of solutions for a generalized Gause type predator prey system was studied.A large number of biological and bioeconomic models are special cases of this system.The system was investigated in the region D={(x,y)|x>0,y>0} because of the biological meaning of the system.The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system,which ensure that the system has at least one limit cycle.The theory of limit sets of autonomous plane systems and the theorem of cycle field of Poincare Bendixson are efficiently employed in the research.The main results and their consequences presented not only generalize some known results,but also improve some corresponding results of other authors.
文摘In this work,we study a predator-prey model of Gause type,in which the prey growth rate is subject to an Allee effect and the action of the predator over the prey is determined by a generalized hyperbolic-type functional response,which is neither differentiable nor locally Lipschitz at the predator axis.This kind of functional response is an extension of the so-called square root functional response,used to model systems in which the prey have a strong herd structure.We study the behavior of the solutions in the first quadrant and the existence of limit cycles.We prove that,for a wide choice of parameters,the solutions arrive at the predator axis in finite time.We also characterize the existence of an equilibrium point and,when it exists,we provide necessary and sufficient conditions for it to be a center-type equilibrium.In fact,we show that the set of parameters that yield a center-type equilibrium,is the graph of a function with an open domain.We also prove that any center-type equilibrium is stable and it always possesses a supercritical Hopf bifurcation.In particular,we guarantee the existence of a unique limit cycle,for small perturbations of the system.
基金funded by National Nature Science Foundation of China,Yunnan Funda-Mental Research Projects,Special Project of Guangdong Province in Key Fields of Ordinary Colleges and Universities and Chaozhou Science and Technology Plan Project of Funder Grant Numbers 82060329,202201AT070108,2023ZDZX2038 and 202201GY01.
文摘The analysis of microstates in EEG signals is a crucial technique for understanding the spatiotemporal dynamics of brain electrical activity.Traditional methods such as Atomic Agglomerative Hierarchical Clustering(AAHC),K-means clustering,Principal Component Analysis(PCA),and Independent Component Analysis(ICA)are limited by a fixed number of microstate maps and insufficient capability in cross-task feature extraction.Tackling these limitations,this study introduces a Global Map Dissimilarity(GMD)-driven density canopy K-means clustering algorithm.This innovative approach autonomously determines the optimal number of EEG microstate topographies and employs Gaussian kernel density estimation alongside the GMD index for dynamic modeling of EEG data.Utilizing this advanced algorithm,the study analyzes the Motor Imagery(MI)dataset from the GigaScience database,GigaDB.The findings reveal six distinct microstates during actual right-hand movement and five microstates across other task conditions,with microstate C showing superior performance in all task states.During imagined movement,microstate A was significantly enhanced.Comparison with existing algorithms indicates a significant improvement in clustering performance by the refined method,with an average Calinski-Harabasz Index(CHI)of 35517.29 and a Davis-Bouldin Index(DBI)average of 2.57.Furthermore,an information-theoretical analysis of the microstate sequences suggests that imagined movement exhibits higher complexity and disorder than actual movement.By utilizing the extracted microstate sequence parameters as features,the improved algorithm achieved a classification accuracy of 98.41%in EEG signal categorization for motor imagery.A performance of 78.183%accuracy was achieved in a four-class motor imagery task on the BCI-IV-2a dataset.These results demonstrate the potential of the advanced algorithm in microstate analysis,offering a more effective tool for a deeper understanding of the spatiotemporal features of EEG signals.
