A Systemic Dynamic Analysis between Higher Education Financial Aid Policies and the Strengthening of Chinese National Community Consciousness

In this paper, the SD model creation method based on the flow rate basic entry tree (RIT) is used to analyze the system dynamics between the college financial aid policy and the strengthening of Chinese national community consciousness [23]. The RIT SD model creation and its application architecture are shown in Figure 3. The SD model constructed by this method contains five components such as flow rate counting tree RIT (including LRX), complex characteristics, SD flow diagram, computable series equations and simulation program.

Figure 3.

Architecture of RIT SD model and its application

By deleting the arc complex point method of decomposition of the SD flow map, the formation of the flow rate number of a unidirectional tree (often called the flow rate into the tree) of the leaves may be other flow rate, if the leaf flow rate by its flow rate into the tree replacement, then the flow rate into the tree of the leaf is not possible to contain the flow rate, it will be the leaf does not contain the flow rate of the flow rate into the tree is called the flow rate basic into the tree (RIT). That is: (1) RIT(t)=(V(t),X(t)||vi(1-M)(t)→R(t)) \[RIT(t)=(V(t),X(t)||{{v}_{i(1-M)}}(t)\to R(t))\] Where: V(t) is the set of variables, X(t) is the set of directed arcs, R(t) ∈ V(t) is the root of the tree, v_i(1–M)(t) ∈ V(t) is the leaves, M is the number of leaves, and t is the time.

In order to separate the material flow and information flow of the object system, SD the cumulative state of the material flow is described by the flow level by the flow rate to describe the process of the material flow accumulation (information flow), all the flow level and flow rate listed in pairs is the flow level and flow rate system. The stream level flow rate system can be described by a 2×N array, denoted as: (2) LRX=[ Rate name1Rate name2⋯Rate nameNStream bit name1Stream bit name2⋯Stream bit nameN ] \[LRX=\left[ \begin{matrix} \text{Rate nam}{{\text{e}}_{1}} & \text{Rate nam}{{\text{e}}_{2}} & \cdots & \text{Rate nam}{{\text{e}}_{N}} \\ \text{Stream bit nam}{{\text{e}}_{1}} & \text{Stream bit nam}{{\text{e}}_{2}} & \cdots & \text{Stream bit nam}{{\text{e}}_{N}} \\ \end{matrix} \right]\] Where the same column flow rate and flow rate is the flow rate and flow rate pairs, i = 1,2,…,N, N is the number of flow rate or flow rate.

If there are a total of N RITs in a RIT component, a branch of any RIT, from the root of the flow rate to all nodes passing through the leaf path of the flow level in order, constitutes a branch vector of L_j(t) → R_i(t), denoted as (Ri(t),Bij(t),L_j(t)), where B_ij(t) is a number of auxiliary variables arranged in order from the root of the tree to the leaves of the tree (i,j = 1,2,…,N). such that d_ij = (R_i(t),B_ij(t),L_j(t)), d_ij can be the sum of multiple branch vectors, i.e., composite branch vectors, and i = j or L_j(t) → R_i(t) branch vectors do not exist, d_ij = 0. Obviously, for the branch vectors (R_i(t),B_ij(t),L_j(t)), if i = j, then R_i(t) and L_j(t) are stream level-flow rate pairs, and this branch vector must form a first-order feedback loop.

By arranging all the branch vectors in a RIT sequentially as matrix rows, with a branch being an element of a matrix row, all the branch vectors in a RIT component can form a branch vector matrix of N×N, i.e.: (3) D0=[ d11d12⋯d1j⋯d1Nd21d22⋯d2j⋯d2N⋮⋮⋮⋮⋮⋮dN1dN2⋯dNj⋯dNN ] \[{{D}_{0}}=\left[ \begin{matrix} {{d}_{11}} & {{d}_{12}} & \cdots & {{d}_{1j}} & \cdots & {{d}_{1N}} \\ {{d}_{21}} & {{d}_{22}} & \cdots & {{d}_{2j}} & \cdots & {{d}_{2N}} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ {{d}_{N1}} & {{d}_{N2}} & \cdots & {{d}_{Nj}} & \cdots & {{d}_{NN}} \\ \end{matrix} \right]\]

Nested operation refers to the method of constructing a complete SD flow graph from a combination of RITs, which in essence is a set of RITs in a RIT component and operation. The embedding operation is usually denoted as U→$\vec{U}$. The embedding operation is performed on the following two RITs: (4) RIT1(t)=(V1(t),E1(t)||v1i(t)→R1(t)) \[RI{{T}_{1}}(t)=({{V}_{1}}(t),{{E}_{1}}(t)||{{v}_{1i}}(t)\to {{R}_{1}}(t))\] (5) RIT2(t)=(V2(t),E2(t)||v2i(t)→R2(t)) \[RI{{T}_{2}}(t)=({{V}_{2}}(t),{{E}_{2}}(t)||{{v}_{2i}}(t)\to {{R}_{2}}(t))\] where: 1i ∈ [1,m₁],2i ∈ [1,m₂].

Then the generated directed graph is denoted as: (6) RITG(t)=(VG(t),EG(t)||vGi(t)→R1(t)∨R2(t)) \[RI{{T}_{G}}(t)=({{V}_{G}}(t),{{E}_{G}}(t)||{{v}_{Gi}}(t)\to {{R}_{1}}(t)\vee {{R}_{2}}(t))\]

Among them: (7) VG(t)=V1(t)∪V2(t)EG(t)=E1(t)∪E2(t)∪(R1→L1)∪(R2→L2)Gi≤m1+m2 $\begin{matrix} {{V}_{G}}(t)={{V}_{1}}(t)\cup {{V}_{2}}(t) \\ {{E}_{G}}(t)={{E}_{1}}(t)\cup {{E}_{2}}(t)\cup ({{R}_{1}}\to {{L}_{1}})\cup ({{R}_{2}}\to {{L}_{2}}) \\ Gi\le {{m}_{1}}+{{m}_{2}} \\ \end{matrix}$

Gi is the number of leaves for generating a directed graph.

In the same RIT component, if there are the same auxiliary variable vertices, they are called duplicate auxiliary variable vertices. Duplicate auxiliary variable vertices cause a large number of repeated calculations, which is not conducive to subsequent simulation calculations. Therefore, it is necessary to simplify the RIT component, and the RIT that does not have duplicate auxiliary variable vertices after simplification is called a simplified RIT.

For n RIT trees in the RIT component, assuming that one of the auxiliary variables U(t) appears j times in total, i.e., there are j duplicate nodes (U₁(t),U₂(t),…,U_j(t)) and each duplicate auxiliary variable has at least two identical child entry trees rooted at it, then take any one of the j duplicate auxiliary variables, assumed to be U_k(t),k ∈ (1,j) and integer, and keep only the child entry tree rooted at U_k. For the other occurrences of duplicate nodes, only that duplicate node is retained, and the branch pointing to it is removed. branch pointing to that node is deleted, and the original duplicate node becomes a leaf node.

When RIT performs embedding operations, it cannot merge the nodes of non-repeating auxiliary variables, and the strong simplification transformation solves this problem well. Strongly simplified transformation is built on the basis of RIT components, and its process includes deleting non-duplicated auxiliary variables and environment variables, and then connecting the undeleted flow position, flow rate and duplicated auxiliary variables according to the connection direction of the original RIT in the direction of the directional path, thus obtaining a strongly simplified RIT. The strongly simplified RIT is thus obtained.The directed graph RITG_(t)$RI{{T}_{\underline{G}}}\left( t \right)$ obtained by nesting the strongly simplified RIT is called the strongly simplified flow graph, and the feedback loops in RITG_(t)$RI{{T}_{\underline{G}}}\left( t \right)$ and the feedback loops of the SD flow graph are one-to-one correspondence. However, using the strongly simplified RIT to compute the feedback loops increases the workload of reducing the feedback loops while reducing the computational workload, so it is only suitable for solving the feedback loops containing the main variables.

In system dynamics, the solution analysis of feedback loop is of great significance for system evaluation and debugging model, etc. Currently, common methods of feedback loop calculation include graphical calculation method and branch-vector determinant method. At present, the common feedback loop calculation methods include graphical calculation method, branch-vector determinant method and branch-vector matrix method.

The branch vector matrix is established by RIT, and the elements on the diagonal of the branch vector matrix are all set to zero, so as to establish the diagonal zero matrix D₁: (8) D1=[ 0d12⋯d1j⋯d1Nd210⋯d2j⋯d2N⋮⋮⋮⋮⋮⋮dN1dN2⋯dNj⋯0 ] \[{{D}_{1}}=\left[ \begin{matrix} 0 & {{d}_{12}} & \cdots & {{d}_{1j}} & \cdots & {{d}_{1N}} \\ {{d}_{21}} & 0 & \cdots & {{d}_{2j}} & \cdots & {{d}_{2N}} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ {{d}_{N1}} & {{d}_{N2}} & \cdots & {{d}_{Nj}} & \cdots & 0 \\ \end{matrix} \right]\] as the second-order sub-branch vector matrix D₂ of D₁: (9) D2=[ 0d12d210 ] \[{{D}_{2}}=\left[ \begin{matrix} 0 & {{d}_{12}} \\ {{d}_{21}} & 0 \\ \end{matrix} \right]\]

Take the elements of the second row of D₂ to form the row matrix E₂ and make the row-zero matrix D2*$D_{2}^{*}$ of D₂: (10) E2=[d210] \[{{E}_{2}}=[\begin{matrix} {{d}_{21}} & 0 \\ \end{matrix}]\] (11) D2*=[ 0d1200 ] \[D_{2}^{*}=\left[ \begin{matrix} 0 & {{d}_{12}} \\ 0 & 0 \\ \end{matrix} \right]\]

Make a branching vector matrix multiplication: (12) E2D2*=[d210][ 0d1200 ]=(0d21×d12) \[{{E}_{2}}{{D}_{2}}^{*}=[\begin{matrix} {{d}_{21}} & 0 \\ \end{matrix}]\left[ \begin{matrix} 0 & {{d}_{12}} \\ 0 & 0 \\ \end{matrix} \right]=(\begin{matrix} 0 & {{d}_{21}}\times {{d}_{12}} \\ \end{matrix})\]

When d₂₁×d₁₂ ≠ 0, its corresponding vector is the computed D₁nd order feedback loop. One by one, the krd order (k = 3,4,…,n)-sub-branch vector matrices of 2 are made: (13) Dk=[ 0d12⋯d1j⋯d1kd210⋯d2j⋯d2k⋮⋮⋮⋮⋮⋮dk1dk2⋯dkj⋯0 ] \[{{D}_{k}}=\left[ \begin{matrix} 0 & {{d}_{12}} & \cdots & {{d}_{1j}} & \cdots & {{d}_{1k}} \\ {{d}_{21}} & 0 & \cdots & {{d}_{2j}} & \cdots & {{d}_{2k}} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ {{d}_{k1}} & {{d}_{k2}} & \cdots & {{d}_{kj}} & \cdots & 0 \\ \end{matrix} \right]\]

Take the elements of row k of D_k to form the row branching vector matrix E_k, and make the row zero matrix Dk*$D_{k}^{*}$ of D_k: (14) Ek=[ dk1dk2…dk(k−1)0 ] \[{{E}_{k}}=\left[ \begin{matrix} {{d}_{k1}} & {{d}_{k2}} & \ldots & {{d}_{k(k-1)}} & 0 \\ \end{matrix} \right]\] (15) Dk*=[ 0d12⋯d1j⋯d1kd210⋯d2j⋯d2k⋮⋮⋮⋮⋮⋮d(k−1)1d(k−1)2⋯d(k−1)j⋯d(k−1)k00⋯000 ] \[D_{k}^{*}=\left[ \begin{matrix} 0 & {{d}_{12}} & \cdots & {{d}_{1j}} & \cdots & {{d}_{1k}} \\ {{d}_{21}} & 0 & \cdots & {{d}_{2j}} & \cdots & {{d}_{2k}} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ {{d}_{(k-1)1}} & {{d}_{(k-1)2}} & \cdots & {{d}_{(k-1)j}} & \cdots & {{d}_{(k-1)k}} \\ 0 & 0 & \cdots & 0 & 0 & 0 \\ \end{matrix} \right]\] k = 2,3,…,N of them.If the rrd element of the Ek×Dk*${{E}_{k}}\times D_{k}^{*}$-row matrix is not 0(r = 1,2,…k – 1), then the r and k stream level rate pairs form a second-order feedback loop. If the sth element of the Ek×Dk*×Dk*${{E}_{k}}\times {{D}_{k}}^{*}\times {{D}_{k}}^{*}$ row matrix is not 0(s = 1,2,…,k – 1) and the rth element of Ek×Dk*${{E}_{k}}\times D_{k}^{*}$ is not 0, then the r,s and k stream level rate pairs form a third order feedback loop. By analogy, a kth order feedback loop can be obtained if Ek×(Dk*)k−1${{E}_{k}}\times {{(D_{k}^{*})}^{k-1}}$.

In the model of Figure 4, universities provide direct financial support to students to ensure that they can complete their studies and promote the strengthening of students’ sense of national community in China. Therefore, the mechanism of strengthening the sense of Chinese national community is as follows: the total amount of financial aid from colleges and universities → economic aid → grants → students’ completion of studies → strengthening the sense of Chinese national community. That is to say, the financial aid used by colleges and universities for economic assistance can reduce the economic pressure on students to complete their studies, realize normal graduation, and promote the enhancement of the consciousness of the Chinese national community, including the students’ sense of identity and sense of belonging to the Chinese national community. On the other hand, the indirect financial assistance provided by colleges and universities to students (e.g. tuition fee remission, work-study assistance, etc.) also promotes the enhancement of students’ sense of Chinese national community. This mechanism can be expressed as follows: the total amount of financial support from colleges and universities → indirect financial support → tuition fee exemption → students’ academic completion → strengthening of the sense of Chinese national community.

The value guidance in the financial aid policy of colleges and universities realizes the ideological and political education in students’ studies from the spiritual level, so as to enhance the students’ sense of identity and sense of belonging to the Chinese national community, i.e., the sense of the Chinese national community is strengthened. The specific mechanism is as follows: the total amount of college financial aid → value guidance → correct three views → ideological and political education → completion of students’ studies → strengthening of the sense of Chinese national community. In the college financial aid policy, with the increase of value guidance work, the correct worldview, life view and value of students can be established, the goal of ideological and political education can be realized, and the strength of the Chinese national community consciousness is thus increased.

In addition to the above direct mechanism of the college financial aid policy on the enhancement of the Chinese national community consciousness, there is also a feedback loop mechanism for the enhancement of the Chinese national community consciousness. The mechanism is described as follows:

(1) Total amount of financial aid for colleges and universities → financial support → grants → completion of studies → strengthening of the sense of community of the Chinese nation.

In the above circular mechanism includes the following 3 steps:

(1) Financial support from universities (including financial support and value guidance) influences the completion of students’ studies, which in turn influences students’ sense of identity and belonging to the Chinese nation.

The initial state of the system model is shown in Figure 7. Among them, (a) ~ (e) represent the intensity of Chinese national community consciousness, college financial aid policy, students’ academic completion, Chinese national sense of belonging and Chinese national identity, respectively.

Figure 7.

Initial state of the system model

As can be seen from Figure 7, the operational results of Chinese national community consciousness intensity demonstrate the dynamic trend of students’ Chinese national community consciousness intensity with the input of college financial aid policies over a systematic operational cycle, with the horizontal coordinate indicating the time (year) and the vertical coordinate indicating the value of each variable. During the period of 2012-2022 shown in the data sample, there are fluctuations in the intensity of Chinese national community consciousness, with an overall upward trend from 2012-2018, a downward trend after 2018, and then an upward trend after 2021. There are two possible reasons for this fluctuation: first, students can enjoy the incentives of multiple college financial aid policies at the same time, so the college financial aid policies enjoyed by students in each year are superpositional, and the impact on the intensity of the Chinese national community consciousness is the result of the accumulation of multiple policies. Secondly, college financial aid policies generally have different life cycles, not only in a single year, there may be a concentration of policies in effect or expiration within a specific period of time, resulting in fluctuations in the curve of the intensity of Chinese national community consciousness.

Comparing the results of the intensity of Chinese national community consciousness with those of college financial aid policies, students’ academic completion, Chinese sense of belonging to the Chinese nation, and Chinese sense of identity, the intensity of Chinese national community consciousness shows the same trend of change as the latter four respectively. When college financial aid policies, students’ academic completion, Chinese sense of belonging and Chinese sense of identity show a significant upward trend, the intensity of Chinese national community consciousness also continues to rise sharply, which further proves the positive influence of college financial aid policies, students’ academic completion, Chinese sense of belonging and Chinese sense of identity on the intensity of students’ Chinese national community consciousness.

In order to test the influence of college financial aid policy on the intensity of Chinese national community consciousness, the value of college financial aid policy is expanded by 1, 2 and 3 times for simulation, and the comparison of simulation results in different contexts is shown in Figure 8. Where (a)~(d) represent the intensity of Chinese national community consciousness, students’ academic completion, Chinese national sense of belonging and Chinese national identity, respectively. current is the initial state of the system, current1, current2 and current3 correspond to three different contexts, the horizontal coordinate represents the time (year), and the vertical coordinate represents the variables’ values. On the whole, when changing the variable of college financial aid policy, the curves of the intensity of Chinese national community consciousness in each year did not move in parallel, but were related to the baseline value before the change, and the larger the baseline value was, the larger the change in the intensity of Chinese national community consciousness was after the multiplication. In addition, with the upward fluctuation of the college financial aid policy variables, the consequent displacement of students’ academic completion, Chinese national sense of belonging, and Chinese national sense of identity varied in size.With the increase of the upward fluctuation, the sense of belonging to the Chinese nation and the sense of Chinese national identity are more apparent than with the increase of students’ academic completion.

Figure 8.

Comparison of simulation results in different scenarios

Therefore, when colleges and universities increase the strength of their financial aid policy support for students, the impact on the intensity of students’ sense of Chinese national community is affected by the baseline value of the college financial aid policy variables, and as the college financial aid policy variables increase, the intensity of the sense of Chinese national community shows a more pronounced strengthening. At the same time, its impact on students’ sense of belonging to and identification with the Chinese nation is greater than that of their academic completion.