The Experts below are selected from a list of 276 Experts worldwide ranked by ideXlab platform
Erwin Frey - One of the best experts on this subject based on the ideXlab platform.
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Topologically robust zero-sum games and Pfaffian orientation: How network topology determines the long-time dynamics of the antisymmetric Lotka-Volterra Equation
Physical Review E, 2018Co-Authors: Philipp Geiger, Johannes Knebel, Erwin FreyAbstract:To explore how the topology of interaction networks determines the robustness of dynamical systems, we study the antisymmetric Lotka-Volterra Equation (ALVE). The ALVE is the replicator Equation of zero-sum games in evolutionary game theory, in which the strengths of pairwise interactions between strategies are defined by an antisymmetric matrix such that typically some strategies go extinct over time. Here we show that there also exist topologically robust zero-sum games, such as the rock-paper-scissors game, for which all strategies coexist for all choices of interaction strengths. We refer to such zero-sum games as coexistence networks and construct coexistence networks with an arbitrary number of strategies. By mapping the long-time dynamics of the ALVE to the algebra of antisymmetric matrices, we identify simple graph-theoretical rules by which coexistence networks are constructed. Examples are triangulations of cycles characterized by the golden ratio phi = 1.6180 ..., cycles with complete subnetworks, and non-Hamiltonian networks. In graph-theoretical terms, we extend the concept of a Pfaffian orientation from even-sized to odd-sized networks. Our results show that the topology of interaction networks alone can determine the long-time behavior of nonlinear dynamical systems, and may help to identify robust network motifs arising, for example, in ecology.
Anna Karczewska - One of the best experts on this subject based on the ideXlab platform.
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Properties of convolutions arising in stochastic Volterra Equations
International Journal of Contemporary Mathematical Sciences, 2007Co-Authors: Anna KarczewskaAbstract:The aim of this note is to provide some results for stochastic convolutions corresponding to stochastic Volterra Equations in separable Hilbert space. We study convolution of the form WΨ(t) := ∫ t 0 S(t− τ)Ψ(τ)dW (τ), t ≥ 0, where S(t), t ≥ 0, is so-called resolvent for Volterra Equation considered,Ψ is an appropriate process and W is a cylindrical Wiener process. Abbr. title: Stochastic Volterra Convolutions
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On stochastic fractional Volterra Equations in Hilbert space
arXiv: Probability, 2006Co-Authors: Anna Karczewska, Carlos LizamaAbstract:In this paper stochastic Volterra Equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties of stochastic convolutions are given. The paper provides a sufficient condition for a stochastic convolution to be a strong solution to a stochastic Volterra Equation.
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Properties of convolutions arising in stochastic Volterra Equations
arXiv: Probability, 2004Co-Authors: Anna KarczewskaAbstract:The aim of this note is to provide some results for stochastic convolutions corresponding to stochastic Volterra Equations in separable Hilbert space. We study convolution of the form $W^{\Psi}(t):=\int_0^t S(t-\tau)\Psi(\tau)dW(\tau)$, $t\geq 0$, where $S(t), t\geq 0$, is so-called {\em resolvent} for Volterra Equation considered,$\Psi$ is an appropriate process and $W$ is a cylindrical Wiener process.
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Stochastic Volterra convolution with Lévy process
2004Co-Authors: Anna KarczewskaAbstract:In the paper we study stochastic convolution appearing in Volterra Equation driven by so called Lévy process. By Lévy process we mean a process with homogeneous independent increments, continuous in probability and cadlag.
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On the Limit Measure to Stochastic Volterra Equations
Journal of Integral Equations and Applications, 2003Co-Authors: Anna KarczewskaAbstract:The paper is concerned with a limit measure of stochastic Volterra Equation driven by a spatially homogeneous Wiener process with values in the space of real tempered distributions. Necessary and sufficient conditions for the existence of the limit measure are provided and a form of any limit measure is given as well.
Philipp Geiger - One of the best experts on this subject based on the ideXlab platform.
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Topologically robust zero-sum games and Pfaffian orientation: How network topology determines the long-time dynamics of the antisymmetric Lotka-Volterra Equation
Physical Review E, 2018Co-Authors: Philipp Geiger, Johannes Knebel, Erwin FreyAbstract:To explore how the topology of interaction networks determines the robustness of dynamical systems, we study the antisymmetric Lotka-Volterra Equation (ALVE). The ALVE is the replicator Equation of zero-sum games in evolutionary game theory, in which the strengths of pairwise interactions between strategies are defined by an antisymmetric matrix such that typically some strategies go extinct over time. Here we show that there also exist topologically robust zero-sum games, such as the rock-paper-scissors game, for which all strategies coexist for all choices of interaction strengths. We refer to such zero-sum games as coexistence networks and construct coexistence networks with an arbitrary number of strategies. By mapping the long-time dynamics of the ALVE to the algebra of antisymmetric matrices, we identify simple graph-theoretical rules by which coexistence networks are constructed. Examples are triangulations of cycles characterized by the golden ratio phi = 1.6180 ..., cycles with complete subnetworks, and non-Hamiltonian networks. In graph-theoretical terms, we extend the concept of a Pfaffian orientation from even-sized to odd-sized networks. Our results show that the topology of interaction networks alone can determine the long-time behavior of nonlinear dynamical systems, and may help to identify robust network motifs arising, for example, in ecology.
Carlos Lizama - One of the best experts on this subject based on the ideXlab platform.
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On stochastic fractional Volterra Equations in Hilbert space
arXiv: Probability, 2006Co-Authors: Anna Karczewska, Carlos LizamaAbstract:In this paper stochastic Volterra Equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties of stochastic convolutions are given. The paper provides a sufficient condition for a stochastic convolution to be a strong solution to a stochastic Volterra Equation.
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a characterization of uniform continuity for Volterra Equations in hilbert spaces
Proceedings of the American Mathematical Society, 1998Co-Authors: Carlos LizamaAbstract:We show that the norm continuity of the resolvent for a Volterra Equation of scalar type is equivalent to the decay to zero of a holomorphic operator family along some imaginary axis.
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Uniform continuity and compactness for resolvent families of operators
Acta Applicandae Mathematica, 1995Co-Authors: Carlos LizamaAbstract:We characterize the uniform continuity and the compactness of a resolvent family of operators {R(t)_t⩾0 for a Volterra Equation of convolution type denned in a Banach space X. In particular, we extend similar results to those for semigroups of operators and cosine families of operators studied in other works.
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On Volterra Equations associated with a linear operator
Proceedings of the American Mathematical Society, 1993Co-Authors: Carlos LizamaAbstract:In this work we define the Hille-Yosida space, in the sense of S. Kantorovitz, for a Volterra Equation of convolution type
Johannes Knebel - One of the best experts on this subject based on the ideXlab platform.
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Topologically robust zero-sum games and Pfaffian orientation: How network topology determines the long-time dynamics of the antisymmetric Lotka-Volterra Equation
Physical Review E, 2018Co-Authors: Philipp Geiger, Johannes Knebel, Erwin FreyAbstract:To explore how the topology of interaction networks determines the robustness of dynamical systems, we study the antisymmetric Lotka-Volterra Equation (ALVE). The ALVE is the replicator Equation of zero-sum games in evolutionary game theory, in which the strengths of pairwise interactions between strategies are defined by an antisymmetric matrix such that typically some strategies go extinct over time. Here we show that there also exist topologically robust zero-sum games, such as the rock-paper-scissors game, for which all strategies coexist for all choices of interaction strengths. We refer to such zero-sum games as coexistence networks and construct coexistence networks with an arbitrary number of strategies. By mapping the long-time dynamics of the ALVE to the algebra of antisymmetric matrices, we identify simple graph-theoretical rules by which coexistence networks are constructed. Examples are triangulations of cycles characterized by the golden ratio phi = 1.6180 ..., cycles with complete subnetworks, and non-Hamiltonian networks. In graph-theoretical terms, we extend the concept of a Pfaffian orientation from even-sized to odd-sized networks. Our results show that the topology of interaction networks alone can determine the long-time behavior of nonlinear dynamical systems, and may help to identify robust network motifs arising, for example, in ecology.
