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1

The existence and stability of spike equilibria in the one-dimensional Gray–Scott model on a finite domain

Theodore Kolokolnikov, Michael J. Ward, Juncheng Wei

Journal:

Applied Mathematics Letters

Year:

2005

Language:

english

File:

PDF, 173 KB

english, 2005

2

Stability of Spiky Solutions in a Competition Model with Cross-Diffusion

Kolokolnikov, Theodore, Wei, Juncheng

Journal:

SIAM Journal on Applied Mathematics

Year:

2011

Language:

english

File:

PDF, 1.68 MB

english, 2011

3

Crime Modeling with Lévy Flights

Chaturapruek, Sorathan, Breslau, Jonah, Yazdi, Daniel, Kolokolnikov, Theodore, McCalla, Scott G.

Journal:

SIAM Journal on Applied Mathematics

Year:

2013

Language:

english

File:

PDF, 377 KB

english, 2013

4

The Stability of a Stripe for the Gierer--Meinhardt Model and the Effect of Saturation

Kolokolnikov, Theodore, Sun, Wentao, Ward, Michael, Wei, Juncheng

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2006

Language:

english

File:

PDF, 1.99 MB

english, 2006

5

Basic Mechanisms Driving Complex Spike Dynamics in a Chemotaxis Model with Logistic Growth

Kolokolnikov, Theodore, Wei, Juncheng, Alcolado, Adam

Journal:

SIAM Journal on Applied Mathematics

Year:

2014

Language:

english

File:

PDF, 688 KB

english, 2014

6

A local PDE model of aggregation formation in bacterial colonies

Chavy-Waddy, Paul-Christopher, Kolokolnikov, Theodore

Journal:

Year:

2016

Language:

english

File:

PDF, 748 KB

english, 2016

7

Mathematics on the Chopping Block

Kolokolnikov, Theodore

Journal:

The Mathematical Intelligencer

Year:

2017

Language:

english

File:

PDF, 3.66 MB

english, 2017

8

Equilibria for an Aggregation Model with Two Species

Evers, Joep H. M., Fetecau, Razvan C., Kolokolnikov, Theodore

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2017

Language:

english

File:

PDF, 1.54 MB

english, 2017

9

The Q-switching instability in passively mode-locked lasers

Theodore Kolokolnikov, Michel Nizette, Thomas Erneux, Nicolas Joly, Serge Bielawski

Journal:

Physica D: Nonlinear Phenomena

Year:

2006

Language:

english

File:

PDF, 680 KB

english, 2006

10

Existence and stability analysis of spiky solutions for the Gierer–Meinhardt system with large reaction rates

Theodore Kolokolnikov, Juncheng Wei, Matthias Winter

Journal:

Physica D: Nonlinear Phenomena

Year:

2009

Language:

english

File:

PDF, 854 KB

english, 2009

11

Phytoplankton depth profiles and their transitions near the critical sinking velocity

Theodore Kolokolnikov, Chunhua Ou, Yuan Yuan

Journal:

Journal of Mathematical Biology

Year:

2009

Language:

english

File:

PDF, 341 KB

english, 2009

12

The existence and stability of spike equilibria in the one-dimensional Gray–Scott model: The pulse-splitting regime

Theodore Kolokolnikov, Michael J. Ward, Juncheng Wei

Journal:

Physica D: Nonlinear Phenomena

Year:

2005

Language:

english

File:

PDF, 600 KB

english, 2005

13

Pulse-Splitting for Some Reaction-Diffusion Systems in One-Space Dimension

Theodore Kolokolnikov, Michael J. Ward, Juncheng Wei

Journal:

Studies in Applied Mathematics

Year:

2005

Language:

english

File:

PDF, 599 KB

english, 2005

14

The Existence and Stability of Spike Equilibria in the One-Dimensional Gray–Scott Model: The Low Feed-Rate Regime

Theodore Kolokolnikov, Michael J. Ward, Juncheng Wei

Journal:

Studies in Applied Mathematics

Year:

2005

Language:

english

File:

PDF, 472 KB

english, 2005

15

Smoke-Ring Solutions of Gierer–Meinhardt System in $\mathbb{R}^{3}$

Kolokolnikov, Theodore, Ren, Xiaofeng

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2011

Language:

english

File:

PDF, 475 KB

english, 2011

16

Introduction: Dissipative localized structures in extended systems

Tlidi, Mustapha, Taki, Majid, Kolokolnikov, Theodore

Journal:

Chaos An Interdisciplinary Journal of Nonlinear Science

Year:

2007

Language:

english

File:

PDF, 668 KB

english, 2007

17

On large ring solutions for Gierer–Meinhardt system in

Kolokolnikov, Theodore, Wei, Juncheng, Yang, Wen

Journal:

Journal of Differential Equations

Year:

2013

Language:

english

File:

PDF, 371 KB

english, 2013

18

Swarming on Random Graphs

James von Brecht, Theodore Kolokolnikov…

Journal:

Journal of Statistical Physics

Year:

2013

Language:

english

File:

PDF, 877 KB

english, 2013

19

Emergent behaviour in multi-particle systems with non-local interactions

Kolokolnikov, Theodore, Carrillo, José A., Bertozzi, Andrea, Fetecau, Razvan, Lewis, Mark

Journal:

Physica D: Nonlinear Phenomena

Year:

2013

Language:

english

File:

PDF, 186 KB

english, 2013

20

Singular patterns for an aggregation model with a confining potential

Kolokolnikov, Theodore, Huang, Yanghong, Pavlovski, Mark

Journal:

Physica D: Nonlinear Phenomena

Year:

2013

Language:

english

File:

PDF, 1.22 MB

english, 2013

21

Simple PDE Model of Spot Replication in Any Dimension

Chen, Chiun-Chuan, Kolokolnikov, Theodore

Journal:

SIAM Journal on Mathematical Analysis

Year:

2012

Language:

english

File:

PDF, 644 KB

english, 2012

22

Spot Deformation and Replication in the Two-Dimensional Belousov-Zhabotinski Reaction in a Water-in-Oil Microemulsion

Kolokolnikov, Theodore, Tlidi, Mustapha

Journal:

Physical Review Letters

Year:

2007

Language:

english

File:

PDF, 379 KB

english, 2007

23

Stability of ring patterns arising from two-dimensional particle interactions

Kolokolnikov, Theodore, Sun, Hui, Uminsky, David, Bertozzi, Andrea L.

Journal:

Physical Review E

Year:

2011

Language:

english

File:

PDF, 346 KB

english, 2011

24

Reduced wave Green's functions and their effect on the dynamics of a spike for the Gierer–Meinhardt model

KOLOKOLNIKOV, THEODORE, WARD, MICHAEL J.

Journal:

European Journal of Applied Mathematics

Year:

2003

Language:

english

File:

PDF, 687 KB

english, 2003

25

PREDICTING PATTERN FORMATION IN PARTICLE INTERACTIONS

VON BRECHT, JAMES H., UMINSKY, DAVID, KOLOKOLNIKOV, THEODORE, BERTOZZI, ANDREA L.

Journal:

Mathematical Models and Methods in Applied Sciences

Year:

2012

Language:

english

File:

PDF, 4.82 MB

english, 2012

26

Instability thresholds in the microwave heating model with exponential non-linearity

ALCOLADO, ADAM, KOLOKOLNIKOV, THEODORE, IRON, DAVID

Journal:

European Journal of Applied Mathematics

Year:

2011

Language:

english

File:

PDF, 787 KB

english, 2011

27

First-passage times, mobile traps, and Hopf bifurcations

Tzou, Justin C., Xie, Shuangquan, Kolokolnikov, Theodore

Journal:

Physical Review E

Year:

2014

Language:

english

File:

PDF, 409 KB

english, 2014

28

The search for and classification of integrable Abel ODE classes

Cheb-Terrab, Edgardo S., Kolokolnikov, Theodore, Roche, Austin D.

Journal:

ACM SIGSAM Bulletin

Year:

1999

Language:

english

File:

PDF, 532 KB

english, 1999

29

Patterned vegetation, tipping points, and the rate of climate change

CHEN, YUXIN, KOLOKOLNIKOV, THEODORE, TZOU, JUSTIN, GAI, CHUNYI

Journal:

European Journal of Applied Mathematics

Year:

2015

Language:

english

File:

PDF, 313 KB

english, 2015

30

Moving and jumping spot in a two-dimensional reaction–diffusion model

Xie, Shuangquan, Kolokolnikov, Theodore

Journal:

Year:

2017

Language:

english

File:

PDF, 2.12 MB

english, 2017

31

Critical exponent of a simple model of spot replication

Chen, Chiun-Chuan, Huang, Chih-Chiang, Kolokolnikov, Theodore

Journal:

Journal of Differential Equations

Year:

2017

Language:

english

File:

PDF, 676 KB

english, 2017

32

Agent-based model of the effect of globalization on inequality and class mobility

Evers, Joep H.M., Iron, David, Kolokolnikov, Theodore, Rumsey, John

Journal:

Physica D: Nonlinear Phenomena

Year:

2017

Language:

english

File:

PDF, 1.06 MB

english, 2017

33

Metastable States for an Aggregation Model with Noise

Evers, Joep H. M., Kolokolnikov, Theodore

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2016

Language:

english

File:

PDF, 1000 KB

english, 2016

34

Pattern formation in bacterial colonies with density-dependent diffusion

SMITH-ROBERGE, JULIEN, IRON, DAVID, KOLOKOLNIKOV, THEODORE

Journal:

European Journal of Applied Mathematics

Year:

2018

Language:

english

File:

PDF, 683 KB

english, 2018

35

Multi-vortex crystal lattices in Bose–Einstein condensates with a rotating trap

Xie, Shuangquan, Kevrekidis, Panayotis G., Kolokolnikov, Theodore

Journal:

Proceedings Mathematical Physical & Engineering Sciences

Year:

2018

Language:

english

File:

PDF, 1.11 MB

english, 2018

36

Ring states in swarmalator systems

O'Keeffe, Kevin P., Evers, Joep H. M., Kolokolnikov, Theodore

Journal:

Physical Review E

Year:

2018

Language:

english

File:

PDF, 2.02 MB

english, 2018

37

Pattern Formation in a Reaction-Diffusion System with Space-Dependent Feed Rate

Kolokolnikov, Theodore, Wei, Juncheng

Journal:

Year:

2018

Language:

english

File:

PDF, 4.86 MB

english, 2018

38

Stabilizing a homoclinic stripe

Kolokolnikov, Theodore, Ward, Michael, Tzou, Justin, Wei, Juncheng

Journal:

Philosophical Transactions Mathematical Physical & Engineering Sciences

Year:

2018

Language:

english

File:

PDF, 832 KB

english, 2018

39

Localized outbreaks in an S-I-R model with diffusion

Gai, Chunyi, Iron, David, Kolokolnikov, Theodore

Journal:

Journal of Mathematical Biology

Year:

2020

Language:

english

File:

PDF, 1.13 MB

english, 2020

40

Stable asymmetric spike equilibria for the GiererâMeinhardt model with a precursor field

Kolokolnikov, Theodore, Paquin-Lefebvre, FrÃ©dÃ©ric, Ward, Michael J

Journal:

IMA Journal of Applied Mathematics

Year:

2020

File:

PDF, 1.30 MB

2020

41

Law of mass action and saturation in SIR model with application to Coronavirus modelling

Kolokolnikov, Theodore, Iron, David

Journal:

Infectious Disease Modelling

Year:

2020

File:

PDF, 1.50 MB

2020

42

Spike Dynamics in the Presence of Noise

Gai, Chunyi, Iron, David, Kolokolnikov, Theodore, Rumsey, John

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2020

File:

PDF, 2.67 MB

2020

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