scholarly journals Dynamic Properties of the Solow Model with Increasing or Decreasing Population and Time-to-Build Technology

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Luca Guerrini ◽  
Mauro Sodini
Keyword(s):  
Population Dynamics ◽  
Dynamic Properties ◽  
Hopf Bifurcations ◽  
Solow Model ◽  
Dynamic Features ◽  
Stability Switches ◽  
Time To Build ◽  
Delayed Differential Equations ◽  
Delay Dependent ◽  
Equations With Delay

We introduce a time-to-build technology in a Solow model with nonconstant population. Our analysis shows that the population dynamics may be a source of stability switches and Hopf bifurcations. The analytical results are obtained using the recent technique introduced by Beretta and Kuang (2002) in the studying of delayed differential equations with delay-dependent coefficients in characteristic equation. Numerical simulations are performed in order to illustrate the main dynamic features of the model.

Stability switches and Hopf bifurcations of an isolated population model with delay-dependent parameters

2015 ◽  
Vol 264 ◽  
pp. 99-115
Author(s):  
Min Xiao ◽  
Guoping Jiang ◽  
Lindu Zhao ◽  
Wenying Xu ◽  
Youhong Wan ◽  
...  
Keyword(s):  
Population Model ◽  
Hopf Bifurcations ◽  
Isolated Population ◽  
Stability Switches ◽  
Delay Dependent

scholarly journals Dynamic Properties of the Solow Model with Bounded Technological Progress and Time-to-Build Technology

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Luca Guerrini ◽  
Mauro Sodini
Keyword(s):  
Technological Progress ◽  
Center Manifold ◽  
Dynamic Properties ◽  
Solow Model ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Time To Build ◽  
Form Theory ◽  
The Stability ◽  
Theoretical Results

We introduce a time-to-build technology in a Solow model with bounded technological progress. Our analysis shows that the system may be asymptotically stable, or it can produce stability switches and Hopf bifurcations when time delay varies. The direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. Numerical simulations confirms the theoretical results.

scholarly journals Nonlinear Dynamics in the Solow Model with Bounded Population Growth and Time-to-Build Technology

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Luca Guerrini ◽  
Mauro Sodini
Keyword(s):  
Nonlinear Dynamics ◽  
Population Dynamics ◽  
Population Growth ◽  
Capital Accumulation ◽  
Labour Force ◽  
Birth Date ◽  
Solow Model ◽  
Time To Build ◽  
Cyclical Behaviour

The aim of this paper is to show that the Solow model equipped by realistic assumptions on technology and population dynamics is capable of explaining a well-known stylised fact of growth, that is, the presence of persistent oscillations of demoeconomic variables. In particular, our analysis shows that the coexistence of delays between (i) new investment and production and (ii) the birth date and the recruitment in the labour force is a source of cyclical behaviour in capital accumulation.

scholarly journals Global Stability and Hopf-bifurcation Analysis of Biological Systems using Delayed Extended Rosenzweig-MacArthur Model

2018 ◽  
Vol 12 (2) ◽  
pp. 171
Author(s):  
Enobong E. Joshua ◽  
Cec Ekemini T. Akpan
Keyword(s):  
Experimental Data ◽  
Population Dynamics ◽  
Hopf Bifurcation ◽  
Asymptotic Stability ◽  
Asymptotically Stable ◽  
Stability Switches ◽  
Large Delay ◽  
Local Hopf Bifurcation ◽  
Delay Margin ◽  
Theoretical Results

This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthur Model via Lyapunov-Krasovskii functionals. Frequency sweeping technique ensures stability switches as the delay parameter increases and passes the critical bifurcating threshold.The model exhibits a local Hopf-bifurcation from asymptotically stable oscillatory behaviors to unstable strange chaotic behaviors dependent of the delay parameter values.Hyper-chaotic fluctuations were observed for large delay values far away from the critical delay margin. Numerical simulations of experimental data obtained via non-dimensionalization have shown the applications of theoretical results in ecological population dynamics.

Stability Switches of a Class of Fractional-Delay Systems With Delay-Dependent Coefficients

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
Xinghu Teng ◽  
Zaihua Wang
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Jacobian Determinant ◽  
Stability Switches ◽  
Characteristic Roots ◽  
Fractional Delay ◽  
Analysis Of Stability ◽  
The Stability ◽  
Key Steps ◽  
Delay Dependent

Stability of a dynamical system may change from stable to unstable or vice versa, with the change of some parameter of the system. This is the phenomenon of stability switches, and it has been investigated intensively in the literature for conventional time-delay systems. This paper studies the stability switches of a class of fractional-delay systems whose coefficients depend on the time delay. Two simple formulas in closed-form have been established for determining the crossing direction of the characteristic roots at a given critical point, which is one of the two key steps in the analysis of stability switches. The formulas are expressed in terms of the Jacobian determinant of two auxiliary real-valued functions that are derived directly from the characteristic function, and thus, can be easily implemented. Two examples are given to illustrate the main results and to show an important difference between the fractional-delay systems with delay-dependent coefficients and the ones with delay-free coefficients from the viewpoint of stability switches.

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