Dynamical regimes of four almost identical chemical oscillators coupled via pulse inhibitory coupling with time delay

2016 ◽  
Vol 18 (7) ◽  
pp. 5509-5520 ◽  
Author(s):  
Vladimir K. Vanag ◽  
Pavel S. Smelov ◽  
Vladimir V. Klinshov
Keyword(s):  
Time Delay ◽  
Chemical Oscillators ◽  
Dynamical Regimes ◽  
Inhibitory Coupling

The dynamics of four almost identical pulse coupled chemical oscillators with time delay are systematically studied.

scholarly journals Effects of Vector Maturation Time on the Dynamics of Cassava Mosaic Disease

2021 ◽  
Vol 83 (8) ◽  
Author(s):  
F. Al Basir ◽  
Y. N. Kyrychko ◽  
K. B. Blyuss ◽  
S. Ray
Keyword(s):  
Time Delay ◽  
Plant Density ◽  
Plant Viruses ◽  
Mosaic Disease ◽  
Plant Diseases ◽  
Cassava Mosaic Disease ◽  
Maturation Time ◽  
Negative Effect ◽  
Dynamical Regimes

AbstractMany plant diseases are caused by plant viruses that are often transmitted to plants by vectors. For instance, the cassava mosaic disease, which is spread by whiteflies, has a significant negative effect on plant growth and development. Since only mature whiteflies can contribute to the spread of the cassava mosaic virus, and the maturation time is non-negligible compared to whitefly lifetime, it is important to consider the effects this maturation time can have on the dynamics. In this paper, we propose a mathematical model for dynamics of cassava mosaic disease that includes immature and mature vectors and explicitly includes a time delay representing vector maturation time. A special feature of our plant epidemic model is that vector recruitment is negatively related to the delayed ratio between vector density and plant density. We identify conditions of biological feasibility and stability of different steady states in terms of system parameters and the time delay. Numerical stability analyses and simulations are performed to explore the role of various parameters, and to illustrate the behaviour of the model in different dynamical regimes. We show that the maturation delay may stabilise epidemiological dynamics that would otherwise be cyclic.

TWOFOLD IMPACT OF DELAYED FEEDBACK ON COUPLED OSCILLATORS

2007 ◽  
Vol 17 (07) ◽  
pp. 2517-2530 ◽  
Author(s):  
OLEKSANDR V. POPOVYCH ◽  
VALERII KRACHKOVSKYI ◽  
PETER A. TASS
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Phase Synchronization ◽  
Threshold Value ◽  
Phase Oscillators ◽  
Intermediate Coupling ◽  
Rich Variety ◽  
Dynamical Regimes ◽  
The Impact

We present a detailed bifurcation analysis of desynchronization transitions in a system of two coupled phase oscillators with delay. The coupling between the oscillators combines a delayed self-feedback of each oscillator with an instantaneous mutual interaction. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. We show that an increase of the coupling strength between oscillators may lead to a loss of synchronization. Intriguingly, the delay has a twofold influence on the oscillations: synchronizing for small and intermediate coupling strength and desynchronizing if the coupling strength exceeds a certain threshold value. We show that the desynchronization transition has the form of a crisis bifurcation of a chaotic attractor of chaotic phase synchronization. This study contributes to a better understanding of the impact of time delay on interacting oscillators.

Modelling nonlinear chemical oscillators with inhibitory coupling

2014 ◽  
Author(s):  
Jacob Gold ◽  
Adam Wang ◽  
Camille Girabawe ◽  
Kyle Harrington ◽  
Seth Fraden
Keyword(s):  
Chemical Oscillators ◽  
Inhibitory Coupling

Experimental study on three chemical oscillators coupled with time delay

1994 ◽  
Vol 100 (9) ◽  
pp. 6977-6978 ◽  
Author(s):  
Nobuaki Nishiyama ◽  
Kaori Eto
Keyword(s):  
Experimental Study ◽  
Time Delay ◽  
Chemical Oscillators

Pulse-Coupled Chemical Oscillators with Time Delay

2012 ◽  
Vol 51 (28) ◽  
pp. 6878-6881 ◽  
Author(s):  
Viktor Horvath ◽  
Pier Luigi Gentili ◽  
Vladimir K. Vanag ◽  
Irving R. Epstein
Keyword(s):  
Time Delay ◽  
Chemical Oscillators

Pulse-Coupled Chemical Oscillators with Time Delay

2012 ◽  
Vol 124 (28) ◽  
pp. 6984-6987 ◽  
Author(s):  
Viktor Horvath ◽  
Pier Luigi Gentili ◽  
Vladimir K. Vanag ◽  
Irving R. Epstein
Keyword(s):  
Time Delay ◽  
Chemical Oscillators

Dynamical regimes of four oscillators with excitatory pulse coupling

2017 ◽  
Vol 19 (19) ◽  
pp. 12490-12501 ◽  
Author(s):  
Dmitry A. Safonov ◽  
Vladimir V. Klinshov ◽  
Vladimir K. Vanag
Keyword(s):  
Time Delays ◽  
Chemical Oscillators ◽  
Dynamical Regimes

Dynamics of four almost identical chemical oscillators pulse coupled via excitatory coupling with time delays are systematically studied.

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