Generally, we can be divided physical phenomena into logical static problems and systematic dynamic problems. For instance, the food chain is a representative

closed loop system with invisible feedback elements. However, a serious problem is that modern science treats systematic problems such as the food chain as a nonlinear dynamic problem and attempts to solve it with regressive solution in statistics such as chaos theory. It seems not a reasonable practice. Instead, this study proposes a novel systematic solution as shown in 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, Figure 1(a) is an open loop system and logical problem. Hence, it does not need to be discussed. However, Figure 1(b) and Figure 1(c) are closed loop systems such as food chains or stock markets including other nonlinear systems; these should be solved by dynamic systems analysis theory because they have [an irreversibility] and cannot be solved inverse between input and output and re not proportional to each other. (Remark: This problem was talked by chemist-physicist 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.

(Modeling): If someone who wants to solve a systematic problem, he/she should build a model system as follows. For instance, given a seller’s positive entropy [10] G(s) and buyer’s negative entropy H(s) in a market, similar to the predator-prey relationship in the food chain in Figure 1(b), the total output entropy converges to equilibrium by self-control based on the law of energy conservation such as the law of supply and demand in Appendix. Similarly, climate change, turbulence in nature, organisms in ecosystems, or any other phenomena with

entropy share the same algorithm can be presented as following; output equation y(t) = transfer function F(s) × input equation u(t).

Y ( s ) = F ( s ) × U ( s ) (1)

where [s] is the Laplace operator; G(s) and H(s) are the transfer functions of the system; Y(s) is the output; and U(s) is the input source. If feedback element H(s) = 0, it is an open loop system. If H(s) is not zero, the basic transfer function Equation (2) is the second-order solution of formula as below [7] .

F ( s ) = Y ( s ) U ( s ) = ω 2 s 2 + 2 β ω s + ω 2 (2)

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] ,

y ( t ) = 1 − A ⋅ e − B ⋅ t sin ( W ⋅ t + φ ) (3)

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(b). Assuming the input sets the systems transfer function, readers can observe the basic response behavior on the monitor, as shown in Figure 2(c). Various behaviors were observed, including initial phenomena, periodic sine curves, decreasing periodicity, and irregularity. For further details, watch the video clip provided in Ref. [11] . (Remark: Determinists in modern science are asked to deal and analyze systematic problems with microscopic and dynamic characteristics in a macroscopic and static viewpoint, but it is not reasonable. Thus, there is no reason for non-physics to follow it.)

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.

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:

f ( x ) = L 1 + e x

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] ,

F ( s ) = G ( s ) 1 + G ( S ) = ω s 2 + ω 2

which is derived from Equation (2). (Simulation): we can obtain the basic response function of is y ( t ) = 1 − sin ω t (where ω is constant), as shown in Figure 3(b), which has a periodic function within the sine curve. (Verification): Figure 3(a) and Figure 3(b) are equivalent because is y ( t ) = 1 − sin ω t is dimensionless and we can obtain same sigmoid curve. Hence, this logistic curve theory is not a logical problem but a systematic problem. If the mathematician has known the systematic solution in that time, he can solve this problem perfectly.

Kuhn’s innovation theory [15] is a famous philosophical principle well-established in modern science. However, it is similar to the heliocentric theory developed in the Middle Ages. The scientific revolution encountered extreme opposition when it was first proposed, but it has led to a paradigm shift, with the theory now widely accepted. Finally, it has arrived at a saturated state as the normal sciences. Therefore, it can be described using the following scheme: [scientific revolution—paradigm shift—normal science]. (Modeling) Here, the correlation can be defined as a time series function as Equation (2) assuming a damping factor of 1 (critical damping state) with an output of [7]

Y ( s ) = U ( s ) G ( s ) 1 + G ( s ) H ( s ) = 1 s + 1 s + x

and an original equation of is y ( t ) = 1 − e − x t (where x is constant), as shown in Figure 3(c). This equation is a gradually increases and eventually reaches saturation. It is very significant the result for his assertion. It is like invention (innovation)—paradigm shift—saturation state (normal science). (Verification): As a practical case, mobile technology developed slowly for 150 years with the following sequence: invention—paradigm shift—normal science. Those disagreeing with the result are encouraged to perform their own simulation with MATLAB directly. However, there are several scientific revolutions, including the steam engine, gun powder, fertilizer, semiconductors, internet, and automobiles whose utility slowly increased and converged into a saturated state, and then further into a normal state, as shown in Figure 3(c). Hence, Kuhn’s theory is not a logical problem but a systematic problem. (Remark; if the Kuhn has known the systematic dynamic solution as mentions above, he can successfully solve this problem.)