Minimal probabilistic P systems for modelling ecological systems

Barbuti, Roberto; Bove, Pasquale; Milazzo, Paolo; Pardini, Giovanni

doi:10.1016/j.tcs.2015.07.035

Cited by 13 publications

(13 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us introduce a function 0 ( , ) ( ), . 24Differentiating the equation 24with respect to variable z and taking into consideration (6) and 8 In these models we demonstrated how to find a solution of equation systems with the usage of generating functions, and in this case we found solutions for moments with regard not to their definition, but a partial differential equation for a generating function. It helped us to find solutions for moments easier.…”

Section: With Initial Conditionsmentioning

confidence: 85%

“…Thus, the solution for (6) and (8) It is evident that at every fixed time the formulas (19) and (20) are probability distributions, and also obtained moments with zero initial conditions and in steady-state mode refer to enumerative characters of Bernoulli distribution [23]. That is why the equation system (9) can be considered as formalization of the Bernoulli process with two parameters, digital number of states and continuous time [29].…”

Section: F T S T Z R T T Z T Z Z S T Z R T T Z T R T N Imentioning

confidence: 99%

“…Let ζ be an arbitrary notion characterizing a number of stages required for completion of service in a queueing system. Taking into consideration (6) and (8)…”

Section: With Initial Conditionsmentioning

confidence: 99%

“…Usually such models are formulated from common grounds at the first approximation and reflect a common trend of real process development. Many of them are stochastic and they are effectively described by queueing theory methods that are connected with Markov process in which functions of time representing probability distributions are unknown [1][2][3][4][5][6][7][8][9][10]. Though analytical solutions exist, they are found by approximate methods.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Solution of Stochastic Differential Equations of the Models of Queueing Theory by the Method of Generationg Function

Иванова¹,

Pavskii²,

Pavsky

2016

Science Evolution

View full text Add to dashboard Cite

The object is mathematical models and their formalization by differential equation systems. The aim is to popularize stochastic models and differential equation systems which solution allows an analytical form. A model formulation and a process of finding a solution to equation systems are of interest. In the queueing theory many models are formalized by systems of linear differential equations with one or more parameters in which distribution of states of queueing systems are unknown functions. In such systems Markov processes are often grounding in the theory of differential equations construction; in a special case postulates of Poisson process are used. Analytical solution of equation systems exists but it is hard to find by traditional methods. In our study we offer a method which allows to find an analytical solution not only for probability distribution but also for moments of any order from one equation system. Description of procedure of differential equation generation for moments of random order varieties is presented. The method is based on the usage of generating (characteristic) functions. This method is effective because it allows to find solutions for moments (here it is expectation and variance) without complex probability calculations. It is especially important in empirical researches of systems that consist of many elements. For example, when we analyze function effectiveness of operating and designed scaling computing systems and supercomputers. Three models and their formalization by differential equation systems that correspond to stochastic processes and analytical solutions of diverse complexity are formulated. Connection between stochastic differential equations systems and their solutions with probability distributions that are classical in probability theory is shown.

show abstract

Section: With Initial Conditionsmentioning

confidence: 85%

Section: F T S T Z R T T Z T Z Z S T Z R T T Z T R T N Imentioning

confidence: 99%

“…Let ζ be an arbitrary notion characterizing a number of stages required for completion of service in a queueing system. Taking into consideration (6) and (8)…”

Section: With Initial Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solution of Stochastic Differential Equations of the Models of Queueing Theory by the Method of Generationg Function

Иванова¹,

Pavskii²,

Pavsky

2016

Science Evolution

View full text Add to dashboard Cite

show abstract

“…In the case of the present model, membranes represent regions in a bidimensional space, and the adjacency between membranes in this graph encodes naturally the adjacency between spatial regions. Likewise, objects are a natural manner to encode discrete entities such as animals or groups of animals [3,18,19,34].…”

Section: Methodsmentioning

confidence: 99%

Modeling diel vertical migration with membrane computing

et al. 2020

View full text Add to dashboard Cite

Diel vertical migration (DVM) is an important ecological phenomenon in which zooplankton migrate vertically to deal with trade-offs associated with greater food availability in shallow waters and lower predator risk in deep waters due to lower light availability. Because of these trade-offs, DVM dynamics are particularly sensitive to changes in light intensity at the water surface. Therefore, changes in the proportion of cloudy and sunny days have the potential to disrupt DVM dynamics. We propose a new membrane computing model that captures the effect of cloud cover on DVM in Daphnia, and we use it to explore the impacts of an increased proportion of cloudy days that are predicted to occur with climate change. Our 2-dimensional, spatially explicit model integrates multiple trophic levels from abiotic nutrients to Daphnia predators. We analyzed the effect that different proportions of cloudy and sunny days throughout the summer have on our model. The model simulations suggest that an increase in sunny days promotes a high phytoplankton concentration near the surface but does not necessarily promote an increased abundance of Daphnia. Our model also suggests that a higher proportion of cloudy days would increase Daphnia abundance due to a shift in the vertical distribution of Daphnia populations towards superficial waters. Our results highlight that climate changes in multiple regions will affect animal migrations leading to altered food web dynamics in freshwater ecosystems, and emphasize the potential of membrane computing as a modeling framework for spatially and temporally explicit ecological processes.

show abstract