TWO NEURON CNNS: SEARCH FOR LIMIT CYCLES

2010 ◽  
Vol 20 (04) ◽  
pp. 1137-1173 ◽  
Author(s):  
XAVIER VILASÍS-CARDONA ◽  
MIREIA VINYOLES-SERRA
Keyword(s):  
Parameter Space ◽  
Limit Cycles ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Parameter Range ◽  
Different Types

In this paper, we show sufficient conditions for the existence of limit cycles in the general continuous time two-neuron autonomous CNN. We find that different types of limit cycles correspond to different regions in the template parameter space. Actually, we are able to predict the CNN behavior from the template values for the full parameter range, except for two small bounded regions.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

scholarly journals The Reduction of Initial Reserves Using the Optimal Reinsurance Chains in Non-Life Insurance

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1350
Author(s):  
Galina Horáková ◽  
František Slaninka ◽  
Zsolt Simonka
Keyword(s):  
Life Insurance ◽  
Continuous Time ◽  
Ruin Probability ◽  
Proportional Reinsurance ◽  
Insurance Risk ◽  
Optimal Reinsurance ◽  
Insurance Contracts ◽  
Time Period ◽  
Different Types ◽  
Capital Injections

The aim of the paper is to propose, and give an example of, a strategy for managing insurance risk in continuous time to protect a portfolio of non-life insurance contracts against unwelcome surplus fluctuations. The strategy combines the characteristics of the ruin probability and the values VaR and CVaR. It also proposes an approach for reducing the required initial reserves by means of capital injections when the surplus is tending towards negative values, which, if used, would protect a portfolio of insurance contracts against unwelcome fluctuations of that surplus. The proposed approach enables the insurer to analyse the surplus by developing a number of scenarios for the progress of the surplus for a given reinsurance protection over a particular time period. It allows one to observe the differences in the reduction of risk obtained with different types of reinsurance chains. In addition, one can compare the differences with the results obtained, using optimally chosen parameters for each type of proportional reinsurance making up the reinsurance chain.

The λ-classification of continuous-time birth-and-death processes

2003 ◽  
Vol 35 (04) ◽  
pp. 1111-1130 ◽  
Author(s):  
Andrew G. Hart ◽  
Servet Martínez ◽  
Jaime San Martín
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Birth And Death Processes ◽  
Positive Recurrent ◽  
Necessary And Sufficient

We study the λ-classification of absorbing birth-and-death processes, giving necessary and sufficient conditions for such processes to be λ-transient, λ-null recurrent and λ-positive recurrent.

scholarly journals Nonfragile H∞ Filter Design for Nonlinear Continuous-Time System with Interval Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Zhongda Lu ◽  
Guoliang Zhang ◽  
Yi Sun ◽  
Jie Sun ◽  
Fangming Jin ◽  
...  
Keyword(s):  
Continuous Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Decoupling Method ◽  
Interval Time ◽  
Time Varying Delay ◽  
Error System ◽  
Delay Dependent

This paper investigates nonfragile H∞ filter design for a class of continuous-time delayed Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Filter parameters occur multiplicative gain variations according to the filter’s implementation, to handle this variations, a nonfragile H∞ filter is presented and a novel filtering error system is established. The nonfragile H∞ filter guarantees the filtering error system to be asymptotically stable and satisfies given H∞ performance index. By constructing a novel Lyapunov-Krasovskii function and using the linear matrix inequality (LMI), delay-dependent conditions are exploited to derive sufficient conditions for nonfragile designing H∞ filter. Using new matrix decoupling method to reduce the computational complexity, the filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

scholarly journals Finite frequency H∞control design for nonlinear systems

2021 ◽  
Vol 12 (1) ◽  
pp. 567
Author(s):  
Zineb Lahlou ◽  
Abderrahim EL-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Control Design ◽  
Loop Model ◽  
Finite Frequency

The work deals finite frequency H<sub>∞</sub> control design for continuous time nonlinear systems, we provide sufficient conditions, ensuring that the closed-loop model is stable. Simulations will be gifted to show level of attenuation that a H<sub>∞</sub> lower can be by our method obtained developed where further comparison.

scholarly journals Limit theorems for some continuous-time random walks

2011 ◽  
Vol 43 (3) ◽  
pp. 782-813 ◽  
Author(s):  
M. Jara ◽  
T. Komorowski
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Quantum Transport ◽  
Continuous Time ◽  
Limit Theorems ◽  
Transport Theory ◽  
Sufficient Conditions ◽  
Continuous Time Random Walks ◽  
Quantum Transport Theory

In this paper we consider the scaled limit of a continuous-time random walk (CTRW) based on a Markov chain {Xn,n≥ 0} and two observables, τ(∙) andV(∙), corresponding to the renewal times and jump sizes. Assuming that these observables belong to the domains of attraction of some stable laws, we give sufficient conditions on the chain that guarantee the existence of the scaled limits for CTRWs. An application of the results to a process that arises in quantum transport theory is provided. The results obtained in this paper generalize earlier results contained in Becker-Kern, Meerschaert and Scheffler (2004) and Meerschaert and Scheffler (2008), and the recent results of Henry and Straka (2011) and Jurlewicz, Kern, Meerschaert and Scheffler (2010), where {Xn,n≥ 0} is a sequence of independent and identically distributed random variables.

scholarly journals Parameter space dimension reduction of an adaptive interpolator during multidimensional signal differential compression

2019 ◽  
pp. 23-30
Author(s):  
A I Maksimov ◽  
M V Gashnikov
Keyword(s):  
Dimension Reduction ◽  
Parameter Space ◽  
Compression Ratio ◽  
Space Dimension ◽  
Computational Experiments ◽  
Parameter Range ◽  
Compression Method ◽  
Multidimensional Signals ◽  
Multidimensional Signal ◽  
Adaptive Interpolator

We propose a new adaptive multidimensional signal interpolator for differential compression tasks. To increase the efficiency of interpolation, we optimize its parameters space by the minimum absolute interpolation error criterion. To reduce the complexity of interpolation optimization, we reduce the dimension of its parameter range. The correspondence between signal samples in a local neighbourhood is parameterized. Besides, we compare several methods for such parameterization. The developed adaptive interpolator is embedded in the differential compression method. Computational experiments on real multidimensional signals confirm that the use of the proposed interpolator can increase the compression ratio.

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