Delay-Induced Excitability

Abstract

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The critical phenomenon and the re-entrance phenomenon in the anti-tumor model induced by the time delay

“…The appearance of the time delay mainly due to finite transmission time related to transport of matter, energy, and information through the system. On the level of a Langevin-type description of a stochastic system, the presence of time delay changes the dynamics of the system, and brings a series of significant and interesting results, such as time delay induced traveling wave solutions [1], coherence resonance [2,3], stochastic resonance [4][5][6], multistability [7], desynchronization [8], excitability [9], periodically oscillate synchronously [10], and critical phenomenon [11].…”

“…It has been realized that time delays are ubiquitous in nature, and delay-induced nonequilibrium phenomena in nonlinear stochastic systems have received a great deal of attention [1][2][3][4][5][6][7][8][9][10][11]. The appearance of the time delay mainly due to finite transmission time related to transport of matter, energy, and information through the system.…”

Influence of Time Delay and Noise on Critical Coupling Parameter in Synchronization of Small World Neural Networks

“…Within the framework of neuron rate-equation models, a recurrent feedback circuit has been studied by adding to the membrane potential equation a term proportional to the potential at an earlier time [20]. This simplified approach has been successful in the understanding of certain characteristic delay-induced phenomena, such as multistability [21,22] and excitability [23]. In addition, delayed feedback in the Fitz Hugh-Nagumo paradigmatic model of excitable systems was shown to increase the coherence and to modulate the main frequencies of the stochastic dynamics in dependence on the feedback delay time [24].…”

Stochastic thermodynamics for delayed Langevin systems

“…On the other hand, in recent decades there has been considerable interest in delayed systems [16][17][18][19][20][21][22][23][24][25][26], whose dynamics are determined by both the present state x ≡ x(t) and the past state x τ ≡ x(t − τ ), where τ > 0 is the delay time. In real systems, delay is usually ascribed to finite speed of transmission of matter or information, or some kind of feedback control.…”

“…In real systems, delay is usually ascribed to finite speed of transmission of matter or information, or some kind of feedback control. It has been shown that delayed systems may exhibit complex dynamic behaviors, such as delay-induced excitability [16] and delay-induced oscillation [17], to list just two. Delayed models have been widely applied to describe * hzhlj@ustc.edu.cn chemical kinetics [18][19][20], neural networks [21], physiological systems [22], optical devices [23,24], population dynamics [25], economic systems [26], and so on.…”