The financial system is a complex, nonlinear chaotic dynamic system caused by its operating mechanism. Therefore, the application of previous forecasting models cannot explain the existence of various interference factors in the financial market and the chaotic characteristics of the financial system. With the help of financial market stability, the article establishes a series of differential equation models that reflect changes in interest rates in the financial system. The article introduces the factor of macro-control on the premise of respecting market regulation to regulate and intervene in economic relations and economic operation status. We apply the Logistic model and stability theory to analyse the positive equilibrium point characteristics of the system and obtain the interest rate liquidity equation with a time-lag financial network.

#### Keywords

- financial market
- big data
- differential equation model
- stability

#### MSC 2010

- 34K20

Harmonious finance refers to an excellent financial, ecological environment in a region. The banking, securities, insurance and trust industries survive the survival of the fittest under the market mechanism and operate safely and orderly. The money market, capital market and insurance market promote each other. They develop in harmony with the economy, and various relationships are relatively harmonious [1]. Building a unified financial system is an integral part of building a harmonious society. In the 31 years of reform and opening up, Chinese financial industry has achieved considerable development. The financial market has initially established a multi-level financial system with relatively complete categories, flexible mechanisms and certain international competitiveness and conforming to the rules of the market economy. However, Chinese financial industry is still in the process of development, and there are still many imperfections and incoordinations. The mechanism for harmonious development among financial market entities such as banks, credit reporting companies and guarantee companies is incomplete. The cooperative relationship between Chinese banks and foreign banks is not yet sound. Interest disputes between various subjects continue. This unbalanced financial institution directly affects the efficiency of resource allocation in the financial market, and at the same time, reduces the risk prevention capability of the financial industry and hinders the goal of building harmonious finance.

Banks, non-bank financial institutions, bank intermediaries and other entities cooperate and complement each other in an efficient and harmonious financial ecosystem and live in harmony to form a financial symbiosis network. Harmonious symbiosis among various financial entities contributes to the balance of financial ecology, and they promote the sustainable development of the entire economic system [2]. Aiming at the shortcomings of existing research, this article draws on the theory of biological symbiosis to study the formation mechanism of financial symbiosis and the type of symbiosis. At the same time, we use the Logistic model to construct the partial benefit symbiosis and reciprocity symbiosis model of financial symbiosis. The article analyses the stability of the symbiotic relationship and proposes countermeasures and suggestions for developing the symbiotic financial relationship.

In a specific economic environment, legal environment, credit environment, market environment and institutional environment, financial market entities provide financial services based on their interests and behaviours [3]. There are shared interests and survival foundations among all market entities. They participate in the market game while carrying out mutually beneficial cooperation to form a symbiosis and coexistence relationship. For example, guarantee companies provide banks with intermediary services such as verification, notarisation, evaluation, coordination and arbitration in market competition, transaction order and dispute resolution as a third party, but also require banks to provide customer credit information for their services. They and commercial banks are mutually beneficial, and they cannot survive after separation. As a result, a symbiotic coexistence relationship is formed.

The foundation of the symbiotic relationship between the financial market entities lies in a symbiotic matrix between each one and the others. They are mainly complementary resources among financial market entities. To promote the smooth development of symbiosis activities, financial market entities need to develop symbiosis communication methods and mechanisms, such as establishing regular meetings, mutual visits and other communication mechanisms and methods [4]. We can call these communication mechanisms and methods a symbiotic interface. The efficiency and function of the symbiosis interface are the key factors that determine the efficiency of financial symbiosis and the stability of the symbiosis relationship.

Symbiosis energy is a concrete manifestation of the viability and value-added ability of financial symbiosis. In the financial symbiosis relationship, the symbiosis energy mainly refers to the funds provided by the bank to the financial market entities [5]. The business development, the improvement of management ability, the enhancement of the ability to resist risks, and net profit increase. The characteristic value of the symbiosis interface and the degree of symbiosis are two key variables that affect the energy of the symbiosis. The characteristic value of the symbiosis interface is an important parameter to measure the communication resistance on the symbiosis interface. The more symbiotic the interfaces, the larger the contact surface and the better the contact medium, the smaller the communication resistance, and the closer the corresponding characteristic value is to zero. In addition, the greater the degree of symbiosis, the greater the energy of symbiosis. The level of symbiotic energy is the prerequisite for the continuous development of symbiotic relationships.

According to the differences in the energy distribution of financial market entities, we divide the financial symbiosis relationship into two types: favour symbiosis and mutual symbiosis. The symbiosis of partial benefit has the following characteristics: (1) New energy is produced, but one party obtains most of the new energy. (2) The symbiotic relationship is beneficial to one party but not harmful to the other party. (3) There are bilateral two-way exchanges between financial market entities. The reciprocal symbiosis relationship has the following characteristics: (1) New energy is generated, and there is a broad-spectrum distribution of new energy. (2) There is a bilateral exchange mechanism and a multilateral exchange mechanism between the financial market entities. (3) The growth and evolution of financial market entities are synchronised. Figure 1 shows the financial symbiosis relationship.

The harmony and stability of the financial symbiosis relationship are essential for establishing a unified financial system [6]. This article will first construct a model of the financial symbiosis relationship to accurately portray the financial symbiosis relationship and the stable conditions of the financial symbiosis relationship.

(1) The profits of financial market entities can reflect the endogenous and exogenous changes experienced by various financial market entities in the evolution of financial symbiosis. We may explain the evolution process of the symbiosis relationship by describing the profit changes of the main body of the financial market. (2) The profit

The main body of the financial market uses the 1/

In the symbiosis of partial benefits, we call the main body of the financial market that benefits more as the leader and the other party as the dependent. We denote the profit scale of the leader as _{1}(_{2}(_{1} is the amount of production factors taken by the leader. According to the hypothesis of this article, the profit level of the leader can be described as
_{2}. In a market structure where only the dependants exist alone, we can describe the profit level of the dependants as

Before the two financial market entities formed a symbiosis, their profit level satisfies the Logistic model:
_{1}(_{2}(_{1} > 0, _{2} > 0, _{1} is the contribution of the profit level of the financial market entity 1 unit to the profit level of the financial market entity 2. _{2} represents the contribution of the profit level of the financial market entity 2 to the profit level of the financial market entity 1.

Now we use differential equations to solve the stability of the partial benefit symbiosis model.
_{1}(_{3}(0,0) can be obtained by solving the differential equation. We analyse the stability of the above three equilibrium points and find that point _{3} is an unstable point under any conditions. For the balance point _{2} to have practical meaning, it needs to be located in the _{1},_{2} ≥ 0) of the phase plane, and one of the following two conditions must be met:
_{1}^{*}, _{2}^{*} to obtain
_{1} < 1 means that the dependent person's contribution to the leader's profit is relatively small. (2) _{2} > 1 means that the dominant player makes a relatively significant contribution to the profits of the dependents. (3) _{1}_{2} < 1 means that when two financial market entities reach a stable state of symbiosis with partial benefits, _{1} is required to be small and _{2} is large [10]. This requires a larger scale of the leader. When the favoured symbiosis reaches a stable state, the symbiosis energy obtained by the dependent is

Differential equations solve the stability of the reciprocal symbiosis model.
_{1} > 0, _{2} > 0,
_{1}_{2} < 1.

We carry out the first-order Taylor expansion of the differential equations to get
_{1}_{2} < 1. Therefore, to achieve a stable symbiosis, the symbiosis relationship in the mutually beneficial symbiosis model is _{1}_{2} < 1. Considering the symmetry of financial market entities, we can further determine the stable symbiosis condition _{1} < 1,_{2} < 1.

The two conditions that need to be met to achieve a stable reciprocal symbiosis relationship can be explained _{1} < 1, _{2} < 1. indicates that the two financial market entities in a mutually beneficial symbiosis relationship contribute relatively little to each other's output. When the reciprocal symbiosis reaches a stable state, the symbiosis energy obtained by the financial market entity 1 is

In the early stage of financial market opening, due to the Chinese government's policy restrictions on sole proprietorship, foreign financial institutions depended on the legal status of local financial institutions. They need to export a large amount of technology and management experience to local financial institutions. However, the investment of Chinese banks is mostly substitutable. Imitable resources such as business, branches and financial policies, and a symbiotic relationship of partial benefit, has been formed between Chinese and foreign financial institutions. With the gradual liberalisation of Chinese financial market policies, the dependence of foreign financial institutions on the legal status of local financial institutions will gradually decrease [11]. Local financial institutions still rely on foreign financial institutions due to their learning ability and other problems, and so foreign financial institutions require greater control over the symbiotic relationship. This has led to unstable phenomena such as equity changes and mergers and acquisitions.

Financial market entities should cultivate and enhance their core capabilities and reduce their dependence on other financial market entities. As far as Chinese banks are concerned, the following measures can be undertaken:

Form irreplaceable valuable resources and capabilities.

Grasp the advanced management concepts and business models of foreign banks as soon as possible. Only in this way can they become the dominant player in the symbiosis with foreign banks.

The government should strive to improve the financial symbiosis environment and promote the growth of domestic weak financial market entities to achieve the goal of the harmonious development of various financial market entities.

China should speed up establishing a sound credit reporting system, cultivate traditional rating agencies and strengthen the supervision of the credit reporting industry. It is also necessary to promote the establishment of a credit investigation system for small and medium-sized enterprises, and formulate laws and regulations applicable to national credit investigation. China needs to quickly establish a unified management agency for the credit reporting system. In addition, the establishment of a credit guarantee legal system should be accelerated, with regard to the access and exit system of guarantee institutions, capital injection and compensation systems, business scope and operating procedures, risk control and financial systems, industry self-discipline and rights protection systems, government coordination and supervision, etc. Make regulations. In terms of guarantee agencies, China should establish a credit rating system for credit guarantee agencies as soon as possible. The local government will contact a third-party evaluation agency to establish a unified credit rating system approved by the bank for the guarantee agency. We need to find and recommend a group of good guarantee agencies to focus on.

Based on the previous analysis of the stability of the financial symbiosis, partial benefit symbiosis and reciprocity symbiosis model, the author found the following rules. Factors such as the resources, capabilities and scale of financial market entities determine their bargaining power in symbiotic behaviour. The distribution of symbiosis energy needs to match the bargaining power among financial market entities. Such a symbiotic relationship will be stable. Therefore, in the short term, the stability of the symbiotic relationship is determined by whether the bargaining power between the financial market entities matches the symbiotic energy distribution. However, in unequal bargaining power, financial solid market entities are prone to opportunistic behaviour and tend to use coercion, punishment and other means. Weak financial market entities tend to increase their bargaining power.

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