Sergey Vakulenko

Neural networks with prescribed large time behaviour

The generalized Hebb rule (with a non-symmetrical synaptic matrix) allows us to create simple neural networks with complicated large time behaviour. These networks can simulate, in a sense, any dynamics and, in particular, can generate any hyperbolic attractors and invariant sets. The explicit mathematical algorithm allows us, by adjusting the network parameters (the neuron number, coupling matrix and thresholds) to obtain a network with given large time dynamics.

Flexible and robust networks

We consider networks with two types of nodes. The v-nodes, called centers, are hyperconnected and interact with one another via many u-nodes, called satellites. This centralized architecture, widespread in gene networks, possesses two fundamental properties. Namely, this organization creates feedback loops that are capable of generating practically any prescribed patterning dynamics, chaotic or periodic, or having a number of equilibrium states. Moreover, this organization is robust with respect to random perturbations of the system.

On chaos in Lotka?Volterra systems: an analytical approach

In this paper, we study Lotka-Volterra systems with N species and n resources. We show that the long time dynamics of these systems may be complicated. Depending on parameter choice, they can gener ...

Large ecosystems in transition: Bifurcations and mass extinction

We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we introduce a feedback between species abundances and resources via abiotic factors. This model is apparently the first of its kind to include a feedback mechanism coupling climate and population dynamics. Moreover, we take into account self-limitation effects. The model explains the coexistence of many species, yet also displays the possibility of catastrophic bifurcations, where all species become extinct under the influence of abiotic factors. We show that as these factors change there are different regimes of ecosystem behavior, including a possibly chaotic regime when abiotic influences are sufficiently strong.

Bifurcations of the climate system and greenhouse gas emissions

We propose a generalization of the classical Goody model by taking into account greenhouse gas emission effects. We develop an asymptotic approach that allows us to obtain an expression for the greenhouse gas flux via the temperature and fluid fields. We show that there is a possible tipping point in atmospheric dynamics resulting from greenhouse gas emissions, where the climate system becomes bistable under sufficiently intensive greenhouse gas emissions.

Biodiversity, extinctions, and evolution of ecosystems with shared resources

We investigate the formation of stable ecological networks where many species share the same resource. We show that such a stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of coexisting species, and we find a relation describing how many species that may become extinct as a result of a sharp environmental change. We introduce a special parameter that is a combination of species traits and resource characteristics used in the model formulation. This parameter describes the pressure on the system to converge, by extinctions. When that stress parameter is large, we obtain that the species traits are concentrated at certain values. This stress parameter is thereby a parameter that determines the level of final biodiversity of the system. Moreover, we show that the dynamics of this limit system can be described by simple differential equations.

Arctic melt ponds and bifurcations in the climate system

Abstract Understanding how sea ice melts is critical to climate projections. In the Arctic, melt ponds that develop on the surface of sea ice floes during the late spring and summer largely determine their albedo – a key parameter in climate modeling. Here we explore the possibility of a conceptual sea ice climate model passing through a bifurcation point – an irreversible critical threshold as the system warms, by incorporating geometric information about melt pond evolution. This study is based on a bifurcation analysis of the energy balance climate model with ice-albedo feedback as the key mechanism driving the system to bifurcation points.

The influence of environmental forcing on biodiversity and extinction in a resource competition model

In this paper, we study a model of many species that compete, directly or indirectly, for a pool of common resources under the influence of periodic, stochastic, and/or chaotic environmental forcing. Using numerical simulations, we find the number and sequence of species going extinct when the community is initially packed with a large number of species of random initial densities. Thereby, any species with a density below a given threshold is regarded to be extinct.

Optical device accelerating dynamic programming

The subject of this report is the comparison of the conventional deterministic computers versus the analogue computer based on the quantum optical system in resolving some NP-hard computational problems. We describe an optical machine which can be realized physically.

Computational capacity of time-recurrent networks

Time-recurrent networks are considered. Synaptic plasticity is defined by a simple Hebb rule. It is well known that this Hebbian mechanism can support learning and memory. We show that this plasticity is a computational instrument with large possibilities. In particular, the synaptic matrix can store different information, both dynamic and static. For example, the network can perform the Fourier and wavelet transformations and calculate probability distributions of unknown parameters. These networks can analyse and identify dynamics, calculate likelihood, study autoregression etc. They can resolve even more sophisticated problems, for example decoding fractal images.