By Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

Research and regulate of Boolean Networks offers a scientific new method of the research of Boolean regulate networks. the elemental instrument during this technique is a singular matrix product referred to as the semi-tensor product (STP). utilizing the STP, a logical functionality should be expressed as a traditional discrete-time linear approach. within the mild of this linear expression, definite significant matters relating Boolean community topology – mounted issues, cycles, temporary occasions and basins of attractors – will be simply printed through a suite of formulae. This framework renders the state-space method of dynamic keep watch over structures appropriate to Boolean keep watch over networks. The bilinear-systemic illustration of a Boolean regulate community makes it attainable to enquire simple keep watch over difficulties together with controllability, observability, stabilization, disturbance decoupling and so on.

**Read or Download Analysis and Control of Boolean Networks: A Semi-tensor Product Approach PDF**

**Similar system theory books**

**Control Theory and Systems Biology**

A survey of ways engineering strategies from keep watch over and platforms idea can be utilized to aid biologists comprehend the habit of mobile structures.

With many parts of technological know-how achieving throughout their obstacles and turning into progressively more interdisciplinary, scholars and researchers in those fields are faced with options and instruments no longer coated via their specific schooling. specially within the existence- and neurosciences quantitative versions according to nonlinear dynamics and complicated structures have gotten as usually carried out as conventional statistical research.

**Chaotic Logic: Language, Thought, and Reality from the Perspective of Complex Systems Science**

This publication summarizes a community of interrelated principles which i've got constructed, on and off, over the last 8 or ten years. The underlying subject matter is the mental interaction of order and chaos. Or, to place it otherwise, the interaction of deduction and induction. i'll attempt to clarify the connection among logical, orderly, awake, rule-following cause and fluid, self organizing, habit-governed, subconscious, chaos-infused instinct.

- Uncertainty and Communication: New Theoretical Investigations
- Essential Readings in Biosemiotics: Anthology and Commentary
- Differential Equations and Dynamical Systems
- Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues
- Dynamical Inverse Problems: Theory and Application (CISM International Centre for Mechanical Sciences)
- Stability Theory of Switched Dynamical Systems

**Extra resources for Analysis and Control of Boolean Networks: A Semi-tensor Product Approach **

**Sample text**

The element at position [(I, J ), (i, j )] is then I,J = w(I J ),(ij ) = δi,j 1, I = i and J = j, 0, otherwise. 16 1. Letting m = 2, n = 3, the swap matrix W[m,n] can be constructed as follows. Using double index (i, j ) to label its columns and rows, the columns of W are labeled by Id(i, j ; 2, 3), that is, (11, 12, 13, 21, 22, 23), and the rows of W are labeled by Id(j, i; 3, 2), that is, (11, 21, 12, 22, 13, 23). 41), we have (11) (12) (13) (21) (22) (23) ⎡ ⎤ 1 0 0 0 0 0 (11) ⎢ 0 0 0 1 0 0 ⎥ (21) ⎢ ⎥ ⎢ 0 1 0 0 0 0 ⎥ (12) ⎢ ⎥ W[2,3] = ⎢ .

Its rows and columns are labeled by double index (i, j ), the columns are arranged by the ordered multi-index Id(i, j ; m, n), and the rows are arranged by the ordered multi-index Id(j, i; n, m). The element at position [(I, J ), (i, j )] is then I,J = w(I J ),(ij ) = δi,j 1, I = i and J = j, 0, otherwise. 16 1. Letting m = 2, n = 3, the swap matrix W[m,n] can be constructed as follows. Using double index (i, j ) to label its columns and rows, the columns of W are labeled by Id(i, j ; 2, 3), that is, (11, 12, 13, 21, 22, 23), and the rows of W are labeled by Id(j, i; 3, 2), that is, (11, 21, 12, 22, 13, 23).

13) Mg = ⎣ ... ⎦. n n n n r11···1 · · · r11···kn · · · r1k2 ···kn · · · rk1 k2 ···kn Mg is called the payoff matrix of game g. 2 Semi-tensor Product of Matrices We consider the conventional matrix product first. 6 Let U and V be m- and n-dimensional vector spaces, respectively. Assume F ∈ L(U × V , R), that is, F is a bilinear mapping from U × V to R. Denote by {u1 , . . , um } and {v1 , . . , vn } the bases of U and V , respectively. We call S = (sij ) the structure matrix of F , where sij = F (ui , vj ), i = 1, .