scholarly journals Local Stability and Bifurcations in Kaldor Model

2005 ◽  
Vol 13 (1) ◽  
pp. 10-20
Author(s):  
Roman Binter ◽  
Lukáš Vácha
Keyword(s):  
Local Stability ◽  
Stability And Bifurcations

scholarly journals Motion Switching and Chaos of a Particle in a Generalized Fermi-Acceleration Oscillator

2009 ◽  
Vol 2009 ◽  
pp. 1-40 ◽  
Author(s):  
A. C. J. Luo ◽  
Y. Guo
Keyword(s):  
Local Stability ◽  
Analytical Prediction ◽  
Fermi Acceleration ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Dynamical Behaviors ◽  
Global View ◽  
Mapping Structures ◽  
Stability And Bifurcations ◽  
First Time

Dynamic behaviors of a particle (or a bouncing ball) in a generalized Fermi-acceleration oscillator are investigated. The motion switching of a particle in the Fermi-oscillator causes the complexity and unpredictability of motion. Thus, the mechanism of motion switching of a particle in such a generalized Fermi-oscillator is studied through the theory of discontinuous dynamical systems, and the corresponding analytical conditions for the motion switching are developed. From solutions of linear systems in subdomains, four generic mappings are introduced, and mapping structures for periodic motions can be constructed. Thus, periodic motions in the Fermi-acceleration oscillator are predicted analytically, and the corresponding local stability and bifurcations are also discussed. From the analytical prediction, parameter maps of periodic and chaotic motions are achieved for a global view of motion behaviors in the Fermi-acceleration oscillator. Numerical simulations are carried out for illustrations of periodic and chaotic motions in such an oscillator. In existing results, motion switching in the Fermi-acceleration oscillator is not considered. The motion switching for many motion states of the Fermi-acceleration oscillator is presented for the first time. This methodology will provide a useful way to determine dynamical behaviors in the Fermi-acceleration oscillator.

Bifurcation and Stability of Periodic Motions in a Periodically Forced Oscillator With Multiple Discontinuities

2008 ◽  
Vol 4 (1) ◽  
Author(s):  
Albert C. J. Luo ◽  
Mehul T. Patel
Keyword(s):  
Local Stability ◽  
Singularity Theory ◽  
Periodic Motions ◽  
Sliding Motion ◽  
Discontinuous Boundary ◽  
Mapping Structures ◽  
Forced Oscillator ◽  
Local Singularity ◽  
Stability And Bifurcations ◽  
Bifurcation And Stability

The local stability and existence of periodic motions in a periodically forced oscillator with multiple discontinuities are investigated. The complexity of periodic motions and chaos in such a discontinuous system is often caused by the passability, sliding, and grazing of flows to discontinuous boundaries. Therefore, the corresponding analytical conditions for such singular phenomena to discontinuous boundary are presented from the local singularity theory of discontinuous systems. To develop the mapping structures of periodic motions, basic mappings are introduced, and the sliding motion on the discontinuous boundary is described by a sliding mapping. A generalized mapping structure is presented for all possible periodic motions, and the local stability and bifurcations of periodic motions are discussed. From mapping structures, the switching points of periodic motions on the boundaries are predicted analytically. Two periodic motions are presented for illustrations of the passability, sliding, and grazing of periodic motions on the boundary.

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

Natural convection in a rectangular cavity with piece-wise heated vertical walls: multiple states, stability and bifurcations

2002 ◽  
Author(s):  
Vladimir Erenburg ◽  
Alexander Gelfgat ◽  
Eliezer Kit ◽  
Pinhas Z. Bar-Yoseph ◽  
Alexander Solan
Keyword(s):  
Natural Convection ◽  
Rectangular Cavity ◽  
Vertical Walls ◽  
Stability And Bifurcations

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 91
Author(s):  
N. Sene
Keyword(s):  
Caputo Derivative ◽  
Local Stability ◽  
Numerical Scheme ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Maximal Lyapunov Exponent ◽  
Electrical Circuits ◽  
Adaptive Controls ◽  
Liouville Derivative

This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

scholarly journals The dynamics of a Leslie type predator–prey model with fear and Allee effect

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. Vinoth ◽  
R. Sivasamy ◽  
K. Sathiyanathan ◽  
Bundit Unyong ◽  
Grienggrai Rajchakit ◽  
...  
Keyword(s):  
Local Stability ◽  
Allee Effect ◽  
Jacobian Matrix ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Lyapunov Coefficient ◽  
Points Of View ◽  
Two Parameter

AbstractIn this article, we discuss the dynamics of a Leslie–Gower ratio-dependent predator–prey model incorporating fear in the prey population. Moreover, the Allee effect in the predator growth is added into account from both biological and mathematical points of view. We explore the influence of the Allee and fear effect on the existence of all positive equilibria. Furthermore, the local stability properties and possible bifurcation behaviors of the proposed system about positive equilibria are discussed with the help of trace and determinant values of the Jacobian matrix. With the help of Sotomayor’s theorem, the conditions for existence of saddle-node bifurcation are derived. Also, we show that the proposed system admits limit cycle dynamics, and its stability is discussed with the value of first Lyapunov coefficient. Moreover, the numerical simulations including phase portrait, one- and two-parameter bifurcation diagrams are performed to validate our important findings.

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