arXiv subjects

Tianping Chen

Publications and source records attributed to Tianping Chen.

40 records · Page 3Linked to original sources

arXiv2007

Desynchronization of pulse-coupled oscillators with delayed excitatory coupling

Collective behavior of pulse-coupled oscillators has been investigated widely. As an example of pulse-coupled networks, fireflies display many kinds of flashing patterns. Mirollo and Strogatz (1990) proposed a pulse-coupled oscillator model to explain the synchronization of South East Asian fireflies ({\itshape Pteroptyx malaccae}). However, transmission delays were not considered in their model. In fact, the presence of transmission delays can lead to desychronization. In this paper, pulse-coupled oscillator networks with delayed excitatory coupling are studied. Our main result is that under reasonable assumptions, pulse-coupled oscillator networks with delayed excitatory coupling can not achieve complete synchronization, which can explain why another species of fireflies ({\itshape Photinus pyralis}) rarely synchronizes flashing. Finally, two numerical simulations are given. In the first simulation, we illustrate that even if all the initial phases are very close to each other, there could still be big variations in the times to process the pulses in the pipeline. It implies that asymptotical synchronization typically also cannot be achieved. In the second simulation, we exhibit a phenomenon of clustering synchronization.

math.DS↗

arXiv2006

Global Exponential Stability of Almost Periodic Solution for A Large Class of Delayed Dynamical Systems

Research of delayed neural networks with variable self-inhibitions, inter-connection weights, and inputs is an important issue. %In the real world, self-inhibitions, %inter-connection weights, and inputs should vary through time. In In this paper, we discuss a large class of delayed dynamical systems with almost periodic self-inhibitions, inter-connection weights, and inputs. This model is universal and includes delayed systems with time-varying delays, distributed delays as well as combination of both. We prove that under some mild conditions, the system has a unique almost periodic solution, which is globally exponentially stable. We propose a new approach, which is independent of existing theory concerning with existence of almost periodic solution for dynamical systems.

math.DS↗

arXiv2006

On Periodic Dynamical Systems

In this paper, we investigate the existence and the global stability of periodic solution for dynamical systems with periodic interconnections, inputs and self-inhibitions. The model is very general, the conditions are quite weak and the results obtained are universal.

math.DS↗

arXiv2006

Pinning complex Networks by A Simple Controller

In this short paper, we point out that a single local stability controller can pin the complex network to a specified solution (or its equilibrium) of the coupled complex network. A rigorous mathematical proof is given, too.

math-ph↗