On the interpretation of Dirac pulses in differential equations for phase oscillators

Klinshov V. V.; Lücken L.; Feketa P.

doi:10.1063/5.0040995

Publications

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On the interpretation of Dirac pulses in differential equations for phase oscillators

Chaos. 2021. Vol. 31. No. 3. Article 031102.

Klinshov V. V., Lücken L., Feketa P.

In this note, we discuss the usage of the Dirac function in models of phase oscillators with pulsatile inputs. Many authors use a product of the delta function and the phase response curve in the right-hand side of an ordinary differential equation to describe the discontinuous phase dynamics in such systems. We point out that this notation has to be treated with care as it is ambiguous. We argue that the presumably most canonical interpretation does not lead to the intended behavior in many cases.

Research target: Mathematics

Keywords: Differential equations

Относительные аналитические законы взаимности

Осипов Д.В., Математический сборник 2026 Т. 217 № 9 С. 130–146

Изучаются законы взаимности, связанные с комплексными линейными расслоениями на расслоениях на ориентируемые окружности. В частности, доказывается следующий закон взаимности. Пусть B – комплексное многообразие и πi:Mi→B – расслоение на ориентируемые окружности, где индекс i пробегает конечное множество. Пусть Li и Ni – комплексные линейные расслоения на каждом многообразии Mi. Закон взаимности утверждает, что сумма всех элементов (πi)∗(c1(Li)∪c1(Ni)), где (πi)∗ – ...

Added: September 3, 2026

Orbifold Saito theory of A and D type singularities

Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80

Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...

Added: September 1, 2026

Non-axiomatizability of modal predicate logics of Dedekind-complete linear orders with constant domains

Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026

We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...

Added: September 1, 2026

Semi-Interlaced Polytopes

Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187

Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems. Motivated by relaxing the bound dim(F)+1 to dim(F), we ...

Added: August 31, 2026

A new spin on polynomial relations among kappa classes

Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146

We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...

Added: August 31, 2026

Any Topological Recursion on a Rational Spectral Curveis KP Integrable

Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69

We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...

Added: August 31, 2026

Сплетенный мир: кошка перевернулась. Доклад Римскому клубу

Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.

Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...

Added: August 31, 2026

Multiplicity-free products of Schubert divisors

Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786

Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...

Added: August 30, 2026

Mukai models of Fano varieties

Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162

We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...

Added: August 30, 2026

Mukai bundles on Fano threefolds

Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99

We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...

Added: August 30, 2026

Full exceptional collections on the symplectic isotropic Grassmannians

Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211

We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...

Added: August 30, 2026

Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets

Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373

We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...

Added: August 30, 2026

Analog of theta-lifting for a curve over dual numbers over a finite field

Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166

We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...

Added: August 30, 2026

Quasi-periodic structures and "shrimps" in chaos on the example a two-mode van der Pol generator

Kuznetsov A. P., Sataev I. R., Stankevich N., Chaos 2026 Vol. 36 No. 8 Article 083131

A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...

Added: August 30, 2026

Approximation of continuous functions on a compact set by solutions of elliptic equations. Quantitative results.

Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30

We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...

Added: August 29, 2026

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics

Shishkina E., Switzerland: Academic Press, 2020.

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed ...

Added: March 7, 2026

Optimal Monomial Quadratization for ODE Systems

Bychkov A., Pogudin G., , in: International Workshop on Combinatorial Algorithms, 32nd International Workshop, IWOCA 2021, Ottawa, ON, Canada, July 5–7, 2021Vol. 12757.: Springer, 2021. P. 122–136.

Added: September 8, 2021

Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial

American Mathematical Society, 2019.

This is the second of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, ...

Added: August 24, 2019

Vestnik St. Petersburg University: Mathematics

Allerton Press Inc., 2017.

This journal publishes the mathematics section of Series I of the Vestnik (Herald) of St. Petersburg University, and is one of the oldest Russian mathematics journals in English translation. Articles cover the major areas of pure and applied mathematics. Many famous mathematicians are associated with the Faculty of Mathematics and Mechanics at St. Petersburg University, including ...

Added: February 4, 2019