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While some genes interact almost instantaneously, other genes could have time delayed interactions (see Figure 1).
This paper presents a minimal-neural-networks-based design approach for the decentralized output-feedback tracking of uncertain interconnected strict-feedback nonlinear systems with unknown time-varying delayed interactions unmatched in control inputs.
It has also been made clear that ingredients such as disorder (the diversity of neurons and the structure of connections) are very important in determining the asymptotic behaviour, as well as the possible presence of delayed interactions and plasticity [5, 6].
Using Lyapunov stability theorem and the performance function technique, it is shown that all signals of the total controlled closed-loop system are bounded and the transient and steady-state performance bounds of local tracking errors can be preselected by adjusting design parameters independent of delayed interactions.
Our method also detects many long-time delayed interactions.
This will effectively enable this model to capture at most d-step time delayed interactions.
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As the proposed inter-BS synchronization scheme always delays interactions (see Section 3), an analytical convergence study appears infeasible.
CaEs may also functionally protect AChE from insecticide toxicity by direct binding and sequestration, thereby preventing or delaying interaction between the insecticide and AChE (Jokanovic 2001; Maxwell 1992a).
The present work considers neural field models that involve delayed spatial interactions and where the delay may depend on the distance between spatial locations [11, 14, 22].
For example, a three-gene synthetic oscillator based on (non-explicitly delayed) negative interactions alone has been already verified experimentally (the "repressilator" [ 4]; Figure 1H) and its generalization has been studied theoretically [ 48].
Secondly, the appropriate Lyapunov Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions, and the neural networks are employed to approximate the unknown nonlinearities.
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