New Solutions for Systematic Problems Involving Complexity through Program MATLAB Based on Indeterminism for Non-Physicists

Modern science has solved the systematic dynamic problems involving complexity such as complex systems by logical solution algebraically such as the old chaos theory derived from algebraic statistics based on determinism. It is very vague and difficult for us. Moreover, modern science treats systems dynamic problems as logical static problems according to determinism. However, this study proposes a novel solution for systematic problems, it is accomplished by systems analysis theory based on a third science (indeterminism) as it is more precise and easier to understand compared to chaos theory. Furthermore, it is suitable for non-physicists, because it is supported by computer simulations without any mathematical processing. Thus, it can be solved especially regressive systems solution. Therefore, this provided an innovative scientific result to non-physicists for their unsolved systematic problems in modern science.


Introduction
This thesis describes an interdisciplinary scientific study regarding systematic problems involving complexity [1] such as complex systems. However, this is not a regular physical article because this solution is not accomplished by conventional physics based on determinism but indeterminism. Please do not misunderstand. (Remark: this study was completed in 2016 [2] [3]). Perhaps de-terminists will not be pleased with the solution provided herein. There is no problem occurred in it because of no relation with determinists.
Meanwhile, in modern science, there is a high separating wall created by physicists between determinism and non-determinism [4] [5] like physics and non-physics. In particular, this study was accomplished by other systematic dynamic solutions based on non-determinism (indeterminism) (see Table 1). It is more precise and easier to apply compared with chaos theory [6] in mathematics based on determinism. Hence, it is similar to a second solution for complexity. Therefore, many non-physicists, including economists, ecologists, and engineers will greatly welcome another solution. Moreover, they have no reason to object to it, as well as, they have no duty to follow determinism. Nevertheless, other physicists do not welcome it because it is different from conventional physics and it is not relevant to determinism. However, there are no problems, if a physicist does not want it, he/she will just continue using their old chaos theory.
(Remark: If they are not welcome, it will be published in non-physical journals; we need a rational judgement.) Generally, modern science has treated all physical problems as logical problems using the chaos theory as derived from algebraic statistics according to determinism. Nonlinear dynamic problems involving complexity and nonlinearity in indeterminism have been solved algebraically by the statistical program SPSS for a long time. Nevertheless, if complexity is a systematic problem but logical problem, it should be solved by systems analysis theory in other science including the commercial program MATLAB through mathematical modeling. And, it must be solved in the following sequence: mathematical modeling-computer simulation-verification-return. (Remark: Systems cannot be solved algebraically.) Consequently, this study will prove that complexity is characterized as a systematic problem. It proves that complexity is a solvable problem based on the third science. Complexity is not a difficult problem to non-physicists. To help readers understand, this study provides three cases studies: 1) Adam Smith's invisible hand; 2) Logistic curve; 3) Tomas Kuhn's innovation theory in non-physics.

Scientific Background
Generally, we can be divided physical phenomena into logical static problems and systematic dynamic problems. For instance, the food chain is a representative  Table 1 and refers to application example in Appendix.
Meanwhile, we can classify systematic problems such as food chains, stock markets, and global weather as shown in Figures 1(a)-(c) and it can always solve such feedback systems with systems analysis theory (control theory) [7]. Unfortunately, many scientists except control engineers are not familiar with the theory, further, it is a difficult and complex theory. Instead, we must utilize MATLAB [8] to solve the problems without any preliminary knowledge. Thus, non-physicists have no difficulty to solve it.
However, we need to understand the basic concept in the figure. For example, Prigogine in his book, The End of Certainty [9]. He said that modern science has not yet solved the irreversibility in determinism.) Accordingly, systematic dynamic problems that appear in science it must be solved the computer through mathematical modelling.

Mathematical Process and Simulation
where  (2) is the second-order solution of formula as below [7].
where β is the damping factor and ω is the periodical variable. Then, the transformed reversible Laplace transform can be given by y(t) [7], where t is time; A, B, W, and φ are variable constants; and β is the damping factor. Equation (3) is nonlinear as a time series function and is an exponential and periodic function that can never be solved inversely. To build a mathematical model system, the variables in Equation (2) must be determined repeatedly.
(Simulation): The computer software MATLAB, as shown in Figure 2(a), is convenient, easy to use, and accurate, similar to the analog simulator in Figure   2 The response output; basic and random function (brown line is input, blue line is output). Open Journal of Applied Sciences

Results: Application Case Studies
These applications as below cannot be not perfectly solved by logical static solution such as the old chaos theory. However, it can be easily solved by systematic dynamic solution through mathematical modeling and MATLAB, to provide innovative scientific results.

Adam Smith's Invisible Hand and Random Walk
Adam Smith's Invisible Hand [12] is a familiar with economists, likewise, the law of supply and demand in Appendix. If they have a preliminary knowledge regarding systems analytic theory in engineering, they can solve this problem.
(Modeling): If the utility of the supplier and demander in a market or predator-prey correlation is a microscopic dynamic problem in real time, moreover, it is a closed-loop feedback system, as shown in Figure 1(b), it will be converged to an equilibrium state automatically. (Simulation): In this case, it was assumed that the transfer function F(s) of the stock market is the same as the one provided above. (Verification): If the stock price information from external fluctuates continuously, the output of the daily stock price is random walk [13], therefore, it is endlessly changed and converges to steady price by self-controlling. In this case, no one can predict the stock price absolutely. Consequently, the invisible hand is not a logical problem but a systematic problem. Accordingly, economists need not follow up determinism and chaos theory, it must be solved by systematic solution based on a third science.

Logistic Curve in Ecology
The second case is the established logistic curve [14] in ecology, which was devised by the mathematician Verhulst, as shown in Figure 3(a). He asserted that population growth follows a sigmoid curve given by the following equation: which is derived from algebraic statistics based on determinism. (Modeling): This is not a logical problem but a systematic one similar to type (c) in Figure 1.
If the feed volume is constant, its correlation can be described by the following transfer function [7],

Discussion
Generally, determinists have solved several systematic problems including nonlinearity in indeterminism by algebraic statistics based on computer; it is a common sense. However, determinists, as well as, other scientists do not consider Open Journal of Applied Sciences the systematic problem as a closed loop system as shown in Figure 1(b), which means that they are unfamiliar with systems analysis theory according to determinism. This will be serious problem to physicists but non-physicists have no problems. Rather, they welcome it because it is more innovative compared with chaos theory in determinism, hence, they have no reason to object to this advanced solution. Therefore, we must break down the high wall between determinism and indeterminism. Accordingly, the novel solution will contribute to the advancement of science and can explain numerous long-standing problems involving complexity in modern science.
For instance, the famous Lorenz's butterfly effect [16] including stranger-attractor is a representative systematic problem, if readers understand the solution, he/she can solve it using MATLAB. Likewise, non-physicists can solve long-standing unsolved problems in diverse fields such as macroeconomic problems or food chains in ecology, quantum mechanics in nonlinear dynamics, and AI algorithms in engineering. Biomedical sciences and space industrial sciences can apply this approach to solve related complex problems. In addition, it can be applied to quantum computing as well as soft scientific areas that include advanced military, political, social, and trading simulations.

Conclusion
This study presents a new systematic solution based on indeterminism accomplished by other scientific principles such as dynamic systems analysis theory based on a third science (indeterminism), for the first time, and with the support of MATLAB. In particular, this study encourages physicists to study novel systematic solutions and apply it to their discipline because it is more precise and easier to use than the old chaos theory. Hence, it represents a second solution for complexity. Complexity is a solvable problem based on this third science. Therefore, our research will significantly contribute to the development of modern science.