delaycoupled

Delay-coupled oscillators are a type of coupled oscillator system where the coupling between oscillators is mediated by a delay. This delay can be introduced in various ways, such as through a transmission line, a feedback loop, or a digital delay line. The delay-coupled oscillators are widely used in various fields, including physics, engineering, and biology, to study the emergence of complex dynamics and synchronization phenomena.

In delay-coupled oscillators, the coupling term is not instantaneous but is delayed by a certain amount of time. This delay can significantly alter the dynamics of the system, leading to the emergence of new phenomena such as delay-induced synchronization, delay-induced chaos, and delay-induced pattern formation. The delay can also introduce a phase shift between the oscillators, which can be used to control the synchronization and pattern formation in the system.

Delay-coupled oscillators can be modeled using various mathematical tools, such as delay differential equations, maps, and cellular automata. These models can be used to study the dynamics of delay-coupled oscillators and to design delay-coupled oscillator systems for specific applications. For example, delay-coupled oscillators have been used to design delay-coupled laser arrays for high-precision metrology, delay-coupled electronic circuits for secure communication, and delay-coupled biological systems for studying the emergence of complex dynamics in living organisms.

In summary, delay-coupled oscillators are a type of coupled oscillator system where the coupling between oscillators is mediated by a delay. The delay can significantly alter the dynamics of the system, leading to the emergence of new phenomena such as delay-induced synchronization, delay-induced chaos, and delay-induced pattern formation. Delay-coupled oscillators have been widely used in various fields, including physics, engineering, and biology, to study the emergence of complex dynamics and synchronization phenomena.