Applications of the Poincare-Hopf Theorem: Epidemic Models and Lotka-Volterra Systems

QR Code

Applications of the Poincare-Hopf Theorem: Epidemic Models and Lotka-Volterra Systems

This paper focuses on properties of equilibria and their associated regions of attraction for continuous-time nonlinear dynamical systems. The classical Poincar\'e--Hopf Theorem is used to derive a general result providing a sufficient condition for the system to have a unique equilibrium. The...

Full description

Bibliographic Details
Main Authors:	Ye, Mengbin, Liu, J., Anderson, B.D.O., Cao, M.
Format:	Journal Article
Published:	2021
Online Access:	http://purl.org/au-research/grants/arc/DP160104500 http://hdl.handle.net/20.500.11937/83245

Similar Items

On Lotka-Volterra evolution law
by: Mukhamedov, Farrukh, et al.
Published: (2011)

Competitive epidemic spreading over networks
by: Ye, Mengbin, et al.
Published: (2022)

On discrete Lotka-Volterra type models
by: Mukhamedov, Farrukh, et al.
Published: (2012)

Non-ergodic Lotka-Volterra operators
by: Saburov, Mansoor
Published: (2015)

M-Lotka-Volterra type operators
by: Mukhamedov, Farrukh, et al.
Published: (2009)

On dynamics of Lotka-Volterra type operators
by: Mukhamedov, Farrukh, et al.
Published: (2014)

Some examples of Lotka-Volterra type models
by: Mukhamedov, Farrukh, et al.
Published: (2011)

Convergence and equilibria analysis of a networked bivirus epidemic model
by: Ye, Mengbin, et al.
Published: (2022)

A class of nonergodic lotka–volterra operators
by: Saburov, Mansoor
Published: (2015)

Stability and monotonicity of Lotka–Volterra type operators
by: Mukhamedov, Farrukh, et al.
Published: (2017)

Parameter Estimation of Lotka-Volterra Model: A Two-Step Model
by: Haliza, Abdul Rahman, et al.
Published: (2013)

A modified algorithm for the homotopy perturbation method with applications to Lotka-Volterra systems
by: Chowdhury, Md. Sazzad Hossien, et al.
Published: (2010)

On divergence of any order cesaaro mean of lotka-volterra operators
by: Saburov, Mansoor
Published: (2015)

An accurate solution to the Lotka-Volterra equations by modified homotopy perturbation method
by: Chowdhury, Md. Sazzad Hossien, et al.
Published: (2011)

An accurate solution to the Lotka-Volterra equations by modified Homotopy perturbation method
by: Chowdhury, Md. Sazzad Hossien
Published: (2012)

An accurate solution to the nonlinear Lotka-Volterra equations by modified Homotopy Pertubation method
by: Chowdhury, Md. Sazzad Hossien
Published: (2013)

Nonlinear Mapping Convergence and Application to Social Networks
by: Anderson, B.D.O., et al.
Published: (2018)

Mathematical Models of Self-Appraisal in Social Networks
by: Anderson, B.D.O., et al.
Published: (2021)

Recent Advances in the Modelling and Analysis of Opinion Dynamics on Influence Networks
by: Anderson, B.D.O., et al.
Published: (2019)

Distributed feedback control on the SIS network model: An impossibility result
by: Ye, Mengbin, et al.
Published: (2020)

Modelling of individual behaviour in the degroot-friedkin self-appraisal dynamics on social networks
by: Ye, Mengbin, et al.
Published: (2019)

Game-theoretic modeling of collective decision making during epidemics
by: Ye, Mengbin, et al.
Published: (2021)

On the Effects of Heterogeneous Logical Interdependencies in a Multi-Dimensional Opinion Dynamics Model
by: Ye, Mengbin, et al.
Published: (2018)

Computing two dimensional poincare maps for hyperchaotic dynamics
by: Mukherjee, Sayan, et al.
Published: (2017)

A Mean-Field Analysis of a Network Behavioral-Epidemic Model
by: Frieswijk, K., et al.
Published: (2022)

Model-independent trajectory tracking of Euler-Lagrange agents on directed networks
by: Ye, Mengbin, et al.
Published: (2016)

Distributed model-independent consensus of Euler–Lagrange agents on directed networks
by: Ye, Mengbin, et al.
Published: (2017)

Leader Tracking of Euler-Lagrange Agents on Directed Switching Networks Using a Model-Independent Algorithm
by: Ye, Mengbin, et al.
Published: (2019)

Geometry of two-qubit system and hopf fibration
by: Wong, Wen Wei
Published: (2013)

Consensus and Disagreement of Heterogeneous Belief Systems in Influence Networks
by: Ye, Mengbin, et al.
Published: (2020)

An influence network model to study discrepancies in expressed and private opinions
by: Ye, Mengbin, et al.
Published: (2019)

Poincare based PPG signal analysis for varying physiological states
by: Kazmi , Syed Absar, et al.
Published: (2016)

Bearing-Only Measurement Self-Localization, Velocity Consensus and Formation Control
by: Ye, Mengbin, et al.
Published: (2017)

On the Analysis of the DeGroot-Friedkin Model with Dynamic Relative Interaction Matrices
by: Ye, Mengbin, et al.
Published: (2017)

Evolution of Social Power in Social Networks with Dynamic Topology
by: Ye, Mengbin, et al.
Published: (2018)

Modification of social dominance in social networks by selective adjustment of interpersonal weights
by: Ye, Mengbin, et al.
Published: (2017)

Discrete-Time Polar Opinion Dynamics with Heterogeneous Individuals
by: Liu, J., et al.
Published: (2019)

Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature
by: Barnes, Gwendolyn E., et al.
Published: (2016)

Poincare polynomials for Abelian symplectic quotients of pure r-qubits via wall-crossings
by: Molladavoudi, Saeid, et al.
Published: (2015)

Nonassociative geometry in quasi-Hopf representation categories I: bimodules and their internal homomorphisms
by: Barnes, Gwendolyn E., et al.
Published: (2015)