Results 21 to 30 of about 4,616 (166)
Mathematics, 2022 In this paper, we study nonlocal dynamics of a nonlinear delay differential equation. This equation with different types of nonlinearities appears in medical, physical, biological, and ecological applications.
Alexandra Kashchenko
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Entropy, 2023 Integrated information theory (IIT) starts from consciousness itself and identifies a set of properties (axioms) that are true of every conceivable experience. The axioms are translated into a set of postulates about the substrate of consciousness (called a complex), which are then used to formulate a mathematical framework for assessing both the ...
William Marshall +9 more
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Van der Pol Equation with a Large Feedback Delay
Mathematics, 2023 The well-known Van der Pol equation with delayed feedback is considered. It is assumed that the delay factor is large enough. In the study of the dynamics, the critical cases in the problem of the stability of the zero equilibrium state are identified ...
Sergey Kashchenko
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Nonlinear Schrödinger type tetrahedron maps
Nuclear Physics B, 2020 This paper is concerned with the construction of new solutions in terms of birational maps to the functional tetrahedron equation and parametric tetrahedron equation.
S. Konstantinou-Rizos
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Quasinormal Forms for Chains of Coupled Logistic Equations with Delay
Mathematics, 2022 In this paper, chains of coupled logistic equations with delay are considered, and the local dynamics of these chains is investigated. A basic assumption is that the number of elements in the chain is large enough.
Sergey Kashchenko
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Adelic integrable systems [PDF]
Journal of Mathematical Physics, 1995 Incorporating the zonal spherical function (zsf) problems on real and p-adic hyperbolic planes into a Zakharov–Shabat integrable system setting, we find a wide class of integrable evolutions that respect the number-theoretic properties of the zsf problem.
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Asymptotics of Regular and Irregular Solutions in Chains of Coupled van der Pol Equations
Mathematics, 2023 Chains of coupled van der Pol equations are considered. The main assumption that motivates the use of special asymptotic methods is that the number of elements in the chain is sufficiently large.
Sergey Kashchenko
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Infinite Turing Bifurcations in Chains of Van der Pol Systems
Mathematics, 2022 A chain of coupled systems of Van der Pol equations is considered. We study the local dynamics of this chain in the vicinity of the zero equilibrium state.
Sergey Kashchenko
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On the 3D consistency of a Grassmann extended lattice Boussinesq system
Nuclear Physics B, 2020 In this paper, we formulate a “Grassmann extension” scheme for constructing noncommutative (Grassmann) extensions of Yang-Baxter maps together with their associated systems of PΔEs, based on the ideas presented in [15].
Sotiris Konstantinou-Rizos
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Hypercomplex integrable systems [PDF]
Nonlinearity, 1999 In this paper we study hypercomplex manifolds in four dimensions. Rather than using an approach based on differential forms, we develop a dual approach using vector fields. The condition on these vector fields may then be interpreted as Lax equations, exhibiting the integrability properties of such manifolds.
Grant, James D. E., Strachan, I. A. B.
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