scholarly journals Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability

2016 ◽  
pp. 553-565 ◽  
Author(s):  
К.В. Шлюфман ◽  
◽  
Г.П. Неверова ◽  
Е.Я. Фрисман ◽  
◽  
...  
Keyword(s):  
Malthusian Parameter ◽  
Parameter Stability ◽  
Ricker Model

scholarly journals Phase Multistability of Dynamics Modes of the Ricker Model with Periodic Malthusian Parameter

2018 ◽  
Vol 13 (1) ◽  
pp. 68-83
Author(s):  
K.V. Shlufman ◽  
G.P. Neverova ◽  
E.Ya. Frisman
Keyword(s):  
Phase Shift ◽  
Dynamic Mode ◽  
Threshold Values ◽  
Attraction Basin ◽  
Malthusian Parameter ◽  
Ricker Model ◽  
Short Period ◽  
Tangent Bifurcation ◽  
Attraction Basins ◽  
Model Trajectory

The paper investigates the phase multistability of dynamical modes of the Ricker model with 2-year periodic Malthusian parameter. It is shown that both the variable perturbation and the phase shift of the Malthusian parameter can lead to a phase shift or a change in the dynamic mode observed. The possibility of switches between different dynamic modes is due to multistability, since the model has two different stable 2-cycles. The first stable 2-cycle is the result of transcritical bifurcation and is synchronous to the oscillations of the Malthusian parameter. The second stable 2-cycle arises as a result of the tangent bifurcation and is asynchronous to the oscillations of the Malthusian parameter. This indicates that two-year fluctuations in the population size can be both synchronous and asynchronous to the fluctuations in the environment. The phase shift of the Malthusian parameter causes a phase shift in the stable 4-cycle of the first bifurcation series to one or even three elements of the 4-cycle. The phase shift to two elements of this 4-cycle is possible due to a change in the half-amplitude of the Malthusian parameter oscillation or the variable perturbation. At the same time, the longer period of the cycle, the more phases with their attraction basins it has, and the smaller the threshold values above which shift from the attraction basin to another one occur. As a result, in the case of cycles with long period (for example, 8-cycle) perturbations, that stable cycles with short period are able to "absorb", can cause different phase transitions, which significantly complicates the dynamics of the model trajectory and, as a consequence, the identification of the dynamic mode observed.

scholarly journals Dynamic modes of the Ricker model with periodic Malthusian parameter

2017 ◽  
Vol 13 (3) ◽  
pp. 363-380 ◽  
Author(s):  
К.В. Шлюфман ◽  
◽  
Г.П. Неверова ◽  
Е.Я. Фрисман ◽  
◽  
...  
Keyword(s):  
Malthusian Parameter ◽  
Ricker Model

scholarly journals Parameter stability and consistency in an alongshore-current model determined with Markov chain Monte Carlo

2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Stability ◽  
Small Uncertainty ◽  
Best Fit ◽  
Stability And Consistency

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.

Alternative Recruitment Models of Adams River Sockeye Salmon, Oncorhynchus nerka

1987 ◽  
Vol 44 (9) ◽  
pp. 1551-1561 ◽  
Author(s):  
Jeremy S. Collie ◽  
Carl J. Walters
Keyword(s):  
Sockeye Salmon ◽  
Oncorhynchus Nerka ◽  
Status Quo ◽  
Management Policy ◽  
Best Management ◽  
Interaction Terms ◽  
Ricker Model ◽  
The Status ◽  
Stock Recruitment ◽  
High Yields

Despite evidence of depensatory interactions among year-classes of Adams River sockeye salmon (Oncorhynchus nerka), the best management policy is one of equal escapement for all year-classes. We fit alternative models (Ricker model and Larkin model) to 32 yr of stock–recruitment data and checked, using simulation tests, that the significant interaction terms in the Larkin model are not caused by biases in estimating the parameters. We identified a parameter set (Rationalizer model) for which the status quo cyclic escapement policy is optimal, but this set fits the observed data very poorly. Thus it is quite unlikely that the Rationalizer model is correct or that the status quo escapement policy is optimal. Using the fitted stock–recruitment parameters, we simulated the sockeye population under several management policies. The escapement policy optimal under the Ricker model is best overall because of the high yields if it should be correct. If the three stock–recruitment models are equally likely to be correct, the simulations predict that adopting a constant-escapement policy would increase long-term yield 30% over the current policy and that an additional 15% increase in yield could be obtained if the policy were actively adaptive.

scholarly journals Quanto Pricing beyond Black–Scholes

2021 ◽  
Vol 14 (3) ◽  
pp. 136
Author(s):  
Holger Fink ◽  
Stefan Mittnik
Keyword(s):  
Option Pricing ◽  
Goodness Of Fit ◽  
Calibration Procedure ◽  
Barrier Options ◽  
Pricing Models ◽  
Modeling Framework ◽  
Double Barrier ◽  
Parameter Stability ◽  
Comprehensive Data ◽  
Black Scholes

Since their introduction, quanto options have steadily gained popularity. Matching Black–Scholes-type pricing models and, more recently, a fat-tailed, normal tempered stable variant have been established. The objective here is to empirically assess the adequacy of quanto-option pricing models. The validation of quanto-pricing models has been a challenge so far, due to the lack of comprehensive data records of exchange-traded quanto transactions. To overcome this, we make use of exchange-traded structured products. After deriving prices for composite options in the existing modeling framework, we propose a new calibration procedure, carry out extensive analyses of parameter stability and assess the goodness of fit for plain vanilla and exotic double-barrier options.

A note on the subcritical generalized age-dependent branching process

1976 ◽  
Vol 13 (4) ◽  
pp. 798-803 ◽  
Author(s):  
R. A. Doney
Keyword(s):  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Malthusian Parameter ◽  
Age Dependent ◽  
The Mean ◽  
Mean Function ◽  
Necessary And Sufficient

For a subcritical Bellman-Harris process for which the Malthusian parameter α exists and the mean function M(t)∼ aeat as t → ∞, a necessary and sufficient condition for e–at (1 –F(s, t)) to have a non-zero limit is known. The corresponding condition is given for the generalized branching process.

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