Local and global dynamics of Ramsey model: From continuous to discrete time

2018 ◽  
Vol 28 (5) ◽  
pp. 055902 ◽  
Author(s):  
Malgorzata Guzowska ◽  
Elisabetta Michetti
Keyword(s):  
Discrete Time ◽  
Global Dynamics ◽  
Ramsey Model ◽  
Local And Global Dynamics

scholarly journals Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Serena Brianzoni ◽  
Cristiana Mammana ◽  
Elisabetta Michetti
Keyword(s):  
Production Function ◽  
Growth Model ◽  
Discrete Time ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Global Dynamics ◽  
Production Factors ◽  
Local And Global Dynamics ◽  
Complex Features

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings while assuming a nonconcave production function. We prove that complex features exhibited are related both to the structure of the coexixting attractors and to their basins. We also show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained while considering concave production functions.

scholarly journals The thalamic low-threshold Ca 2+ potential: a key determinant of the local and global dynamics of the slow (<1 Hz) sleep oscillation in thalamocortical networks

2011 ◽  
Vol 369 (1952) ◽  
pp. 3820-3839 ◽  
Author(s):  
Vincenzo Crunelli ◽  
Adam C. Errington ◽  
Stuart W. Hughes ◽  
Tibor I. Tóth
Keyword(s):  
Action Potential ◽  
Slow Oscillation ◽  
Global Dynamics ◽  
Action Potential Firing ◽  
Local And Global Dynamics ◽  
Up States ◽  
Potential Firing ◽  
Low Threshold

During non-rapid eye movement sleep and certain types of anaesthesia, neurons in the neocortex and thalamus exhibit a distinctive slow (<1 Hz) oscillation that consists of alternating UP and DOWN membrane potential states and which correlates with a pronounced slow (<1 Hz) rhythm in the electroencephalogram. While several studies have claimed that the slow oscillation is generated exclusively in neocortical networks and then transmitted to other brain areas, substantial evidence exists to suggest that the full expression of the slow oscillation in an intact thalamocortical (TC) network requires the balanced interaction of oscillator systems in both the neocortex and thalamus. Within such a scenario, we have previously argued that the powerful low-threshold Ca 2+ potential (LTCP)-mediated burst of action potentials that initiates the UP states in individual TC neurons may be a vital signal for instigating UP states in related cortical areas. To investigate these issues we constructed a computational model of the TC network which encompasses the important known aspects of the slow oscillation that have been garnered from earlier in vivo and in vitro experiments. Using this model we confirm that the overall expression of the slow oscillation is intricately reliant on intact connections between the thalamus and the cortex. In particular, we demonstrate that UP state-related LTCP-mediated bursts in TC neurons are proficient in triggering synchronous UP states in cortical networks, thereby bringing about a synchronous slow oscillation in the whole network. The importance of LTCP-mediated action potential bursts in the slow oscillation is also underlined by the observation that their associated dendritic Ca 2+ signals are the only ones that inform corticothalamic synapses of the TC neuron output, since they, but not those elicited by tonic action potential firing, reach the distal dendritic sites where these synapses are located.

COMPETITION AND COOPERATION ON PREDATION: BIFURCATION THEORY OF MUTUALISM

2021 ◽  
pp. 1-25
Author(s):  
SRIJANA GHIMIRE ◽  
XIANG-SHENG WANG
Keyword(s):  
Quantitative Information ◽  
Model Systems ◽  
Exclusion Principle ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Severe Condition ◽  
Predator Species ◽  
Competition And Cooperation ◽  
Local And Global Dynamics ◽  
Predator Prey Models

In this paper, we investigate two predator–prey models which take into consideration hunting cooperation (i.e., mutualism) between two different predators and within one predator species, respectively. Local and global dynamics are obtained for the model systems. By a detailed bifurcation analysis, we investigate the dependence of predation dynamics on mutualism (cooperative predation). From our study, we prove that mutualism may enhance the survival of mutualist predators in a severe condition and break the competitive exclusion principle. We further provide quantitative information about how the cooperative predation (mutualism) may (i) establish multiple stability switches on the positive equilibrium; (ii) generate backward bifurcation on equilibria; (iii) induce supercritical or subcritical Hopf bifurcations; and (iv) establish bi-stability phenomenon between the predator-free equilibrium and a positive equilibrium (or a limit cycle).

Local and global dynamics in collective movements of embryonic cells

Biosystems ◽  
2018 ◽  
Vol 173 ◽  
pp. 36-51 ◽  
Author(s):  
Lev V. Beloussov ◽  
Tatiana G. Troshina ◽  
Nadezhda S. Glagoleva ◽  
Stanislav V. Kremnyov
Keyword(s):  
Global Dynamics ◽  
Embryonic Cells ◽  
Local And Global Dynamics ◽  
Collective Movements

scholarly journals Local and Global Dynamics of the G Protein-Coupled Receptor CXCR1

Biochemistry ◽  
2011 ◽  
Vol 50 (12) ◽  
pp. 2371-2380 ◽  
Author(s):  
Sang Ho Park ◽  
Fabio Casagrande ◽  
Bibhuti B. Das ◽  
Lauren Albrecht ◽  
Mignon Chu ◽  
...  
Keyword(s):  
G Protein ◽  
Global Dynamics ◽  
G Protein Coupled Receptor ◽  
Local And Global Dynamics ◽  
G Protein Coupled

Bifurcations and chaos control in a discrete-time biological model

2020 ◽  
Vol 13 (04) ◽  
pp. 2050022 ◽  
Author(s):  
A. Q. Khan ◽  
T. Khalique
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Complex Dynamics ◽  
Small Neighborhood ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Flip Bifurcation ◽  
Time Model ◽  
Predator Prey Model

In this paper, bifurcations and chaos control in a discrete-time Lotka–Volterra predator–prey model have been studied in quadrant-[Formula: see text]. It is shown that for all parametric values, model has boundary equilibria: [Formula: see text], and the unique positive equilibrium point: [Formula: see text] if [Formula: see text]. By Linearization method, we explored the local dynamics along with different topological classifications about equilibria. We also explored the boundedness of positive solution, global dynamics, and existence of prime-period and periodic points of the model. It is explored that flip bifurcation occurs about boundary equilibria: [Formula: see text], and also there exists a flip bifurcation when parameters of the discrete-time model vary in a small neighborhood of [Formula: see text]. Further, it is also explored that about [Formula: see text] the model undergoes a N–S bifurcation, and meanwhile a stable close invariant curves appears. From the perspective of biology, these curves imply that between predator and prey populations, there exist periodic or quasi-periodic oscillations. Some simulations are presented to illustrate not only main results but also reveals the complex dynamics such as the orbits of period-2,3,13,15,17 and 23. The Maximum Lyapunov exponents as well as fractal dimension are computed numerically to justify the chaotic behaviors in the model. Finally, feedback control method is applied to stabilize chaos existing in the model.

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