Differential Equations and Dynamical Systems

By Ferdinand Verhulst. 2012

2,361 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b2bbb969c41b75d3a46bbdc632123712dbc95246

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Chongjie Zhang
2. Jicai Huang
3. Victor R. Lesser
4. Shigui Ruan
5. Igor Mezi'c
6. Remy Magloire Etoua
7. Olga Vasilyeva
8. Salma M. Al-Tuwairqi

In Numerical Analysis

1. Remy Magloire Etoua
2. Olga Vasilyeva
3. Salma M. Al-Tuwairqi
4. Sarah Al-sheikh
5. Syed Abbas
6. Tiago de Carvalho
7. W. Fang
8. Shigui Ruan

In Statistical and Nonlinear Physics

1. Igor Mezi'c
2. Remy Magloire Etoua
3. Olga Vasilyeva
4. Salma M. Al-Tuwairqi
5. Sarah Al-sheikh
6. Syed Abbas
7. Tiago de Carvalho
8. W. Fang

Citations in the corpus

• Bifurcations in a predator–prey system of Leslie type with generalized Holling type III functional response☆ (2014, background): “The results in Bogdanov [3,4] and Takens [35] or Perko [31] imply that system (3.”
• Global Dynamics of a Mathematical Model on Smoking (2014, methodology): “Evaluating the Jacobian matrix of model 3 at E 0 (using linearization method [11]) gives”
• Linearization in the large of nonlinear systems and Koopman operator spectrum (2013, methodology): “This example is taken from the textbook by Lawrence Perko [31]”
• Multi-Agent Learning with Policy Prediction (2010, background): “From dynamical systems theory (Perko 1991), if the matrix U is invertible, qualitative forms of the dynamical system specified by Equation 7 depend on eigenvalues of U , which are given by”
• Bifurcation analysis of a generalized Gause model with prey harvesting and a generalized Holling response function of type III (2010, background): “The monotonous movement of the separatrices is shown for example in [30].”
• Ordinary Differential Equations and Dynamical Systems (2012, neutral): “Classical references include Chicone [6], Guckenheimer and Holmes [12], Hasselblat and Katok [15], [25], Hirsch, Smale, and Devaney [18], Palis and de Melo [33], Perko [34], Robinson [35], [36], Ruelle [38], Verhulst [43], and Wiggins [47], [48].”
• On Poincar\'e-Bendixson Theorem and Non-Trivial Minimal Sets in Planar Nonsmooth Vector Fields (2013, methodology): “Hartman–Grobman Theorem, the Poincaré–Bendixson Theorem, and the Peixoto Theorem among others (see the book [12]).”
• Competition of three species in an advective environment (2012, background): “Thus, all the eigenvalues have negative real parts, which implies asymptotic stability [23].”