Results 1 to 10 of about 4,628 (266)
Symmetries and integrable systems [PDF]
Fundamental ResearchSymmetry plays key roles in modern physics especially in the study of integrable systems because of the existence of infinitely many local and nonlocal generalized symmetries.
Sen-Yue Lou, Bao-Feng Feng
doaj +2 more sources
Pumping approximately integrable systems [PDF]
Nature Communications, 2017 Integrable models have an infinite number of conserved quantities but most realizations suffer from integrability breaking perturbations. Here the authors show that weakly driving such a system by periodic perturbations leads to large nonlinear responses
Florian Lange +2 more
doaj +2 more sources
Travelling Waves in the Ring of Coupled Oscillators with Delayed Feedback
Mathematics, 2023 We studied travelling waves in N nonlinear differential equations with a delay and large parameter. This system is important because it can be regarded as a phenomenological model of N-coupled neuron-like oscillators with delay.
Alexandra Kashchenko +2 more
doaj +1 more source
QUATERNIONIC INTEGRABLE SYSTEMS [PDF]
Symmetry and Perturbation Theory, 2003 Standard (Arnold-Liouville) integrable systems are intimately related to complex rotations. One can define a generalization of these, sharing many of their properties, where complex rotations are replaced by quaternionic ones. Actually this extension is not limited to the integrable case: one can define a generalization of Hamilton dynamics based on ...
Gaeta, G., Morando, P.
openaire +2 more sources
Моделирование и анализ информационных систем, 2020 The logistic equation with delay or Hutchinson’s equation is one of the fundamental equations of population dynamics and is widely used in problems of mathematical ecology.
Sergey D. Glyzin +2 more
doaj +1 more source
Neural systems integration [PDF]
Neurocomputing, 2004 A need is identified to build models of the central nervous system that are semi-complete, applied within multiple contexts to multiple tasks, using methodologies that span multiple levels of abstraction. The issues and constraints in building such models are discussed with respect to completeness, validation, cost, scalability and robustness.
Michael, Arnold +3 more
openaire +2 more sources
On oscillation of solutions of scalar delay differential equation in critical case
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper we study the oscillation problem for the known scalar delay differential equation. We assume that the coefficients of this equation have an oscillatory behaviour with an amplitude of oscillation tending to zero at infinity.
Pavel Nesterov
doaj +1 more source
Relaxation Oscillations in the Logistic Equation with Delay and Modified Nonlinearity
Mathematics, 2023 We consider the dynamics of a logistic equation with delays and modified nonlinearity, the role of which is to bound the values of solutions from above.
Alexandra Kashchenko, Sergey Kashchenko
doaj +1 more source
Local Dynamics of Logistic Equation with Delay and Diffusion
Mathematics, 2021 The behavior of all the solutions of the logistic equation with delay and diffusion in a sufficiently small positive neighborhood of the equilibrium state is studied.
Sergey Kashchenko
doaj +1 more source
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
doaj +1 more source