Effect of time delay in a bistable synthetic gene network

Abstract

The essence of logical stochastic resonance is the dynamic manipulation of potential wells. The effect of time delay on the depth of potential wells and the width of a bistable region can be inferred by logic operations in the bistable system with time delay. In a time-delayed synthetic gene network, time delay in the synthesis process can increase the depth of the potential wells, while that in the degradation process, it can reduce the depth of the potential wells, which will result in a decrease in the width of the bistable region (the reason for time delay to induce logic operations without external driving force) and the instability of the system (oscillation). These two opposite effects imply stretching and folding, leading to complex dynamical behaviors of the system, including period, chaos, bubble, chaotic bubble, forward and reverse period doubling bifurcation, intermittency, and coexisting attractors.

Logical stochastic resonance in a cross-bifurcation non-smooth system

“…In addition, it has been demonstrated that correlated internal and external noises [21][22][23] can also produce logic operations in bistable systems. It has also been shown that other elements can produce logic operations in bistable systems, including system parameters, [24] time delay, [25][26][27] coupling between two subsystems, [28] and periodic and non-periodic forces. [29][30][31] Since three different inputs correspond to two outputs in a bistable system this may cause information to be lost, making XOR logic unattainable.…”

Temperature-induced logical resonance in the Hodgkin–Huxley neuron

“…[13][14][15][16][17][18][19] Noise is not the only factor to induce logical resonance. Periodic force, [20][21][22][23] parameter, [24] time delay, [25][26][27] autapse, [28] coupling, [29,30] and chaotic signal [31,32] can be used as replacements for stochastic noise to obtain similar results with SR. The scope of the research has been extended from typical bistable systems to multi-stable systems in order to explore all types of logical operations.…”

Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system

“…[27] On the other hand, some researchers have carried out LSR-related studies from a theoretical perspective, and confirmed that stochastic noise is not necessary for logical resonance. Many deterministic factors, such as periodic force, [34][35][36][37][38] time delay, [39][40][41][42][43] parameters, [44,45] coupling, [46][47][48] and temperature, [49] can also induce LSR-like phenomena.…”