Sender: Blazer (Blazer), the letter area: Joke Title: Boys chase girls' mathematical model sending station: The Big Green (Mon May 6 10:33:17 2002), transfer
T Al-time A Jun's academic performance is Y (t); its B woman's alienation is X (t); when A Jun has not begun to pursue B women, B women's alienation growth (usually discovered A Nian's bad behavior is in line with the Malthus model, ie DX / DT = AX (T) where A is normal. When Y (t) is present, the value of X (t) and the value of X (t) and the value of X (t) are proportional, and the proportional constant is b, so that DX (t) / dt = ax (t) -bx (t) Y (t). After assume that A Jun started to pursue the attack on B, it immediately turned into a good feeling of blessing A Jun, and set the conversion system to α, and then the A Jun started to B women's offensive, The natural decline rate of the A Jun's school is proportional to the academic performance, the proportional coefficient is E. Thus, DY (T) / DX = αBX (T) Y (t) -e (t) is obtained, and two numbers of two numbers composed of academic and alienation are mutually acting without external interference. : {; DX (T) / DT = AX-BXY; DY (T) / DT = Cxy-Ey. (1)}; where c = αb. This is a non-linear autonomous system, in order to seek two numbers x Y 's variation rules, we have made it a decent analysis. {; Ax-bxy = 0; cxy-Ey = 0.}; The two balanced positions of the essay system (1) are: O (0, 0), M (D / C, A / B). From ( 1) The two gears have removed DT, and the separation variables can be obtained for the first point: f (x, y) = cx-dln|x|-aln | = k. (2) Easy to find a function f (x, y) ) The unique resident point is M (D / C, A / B) Re-use the sufficient condition determination conditions of the extreme value described in Chapter 5. It can be judged that M is the minimum value point of F. Also easy to see, when X → ∞ (bless A Jun Errhea) or Y → ∞ (A Jun is a wood only learning) is f → ∞; and x → 0 (A monarch is deformed Surgery, B woman is no preparation for him); Y → 0 (A king does not study without learning, there is also f → ∞. It is not difficult to see, in the first image internal continuous function, z = The graphic of F (x, y) is a minimum point in m, and in a curved surface that is unlimited in the first to limit, so it is a projection f of the Z = K (K> 0) in the phase flat XO (X, y) = k (k> 0) is a closed curve cluster of the surround point M. This shows that academic performance and alien index are cyclical. From the ecological sense, this is easy to understand. When A Jun's study results decline, the B women will alienate A Jun; so A Jun has begun to work hard, and the learning grade Y (t) has risen. So the B woman has begun to start with A Jun, and he has fallen again. More than a female interaction with B, of course, the time of learning, the A Jun's study grade Y (t) has fallen. However, we can prove that although the closing wires are different, the average number of X and Y in its cycle is a constant, and the two coordinates of the balance point M.
In fact, by the second equation of (1) can be obtained: DY / YDT = CX- E, both ends within one cycle time T, to: ∫ (DY / YDT) DT = C∮xDT-DT (3 Note that when t passs through one cycle T, the points (x, y) wind turns around the clip and return to the initial point, so that ∫ (DY / YDT) DT = ∮DY / Y = 0. So, by (3) Have obtained: (∫XDT) / t = d / c. Similarly, the first equation of (1) can be obtained: (∫YYDT) / t = a / b. Now consider the pursuit of the attack on the above The impact of the model. It is proportional to the alienation of the pursuit of attack and the moment, and the proportional coefficient is H, and h reflects the role of pursuit of offensive. In this case, the model should be changed to: {; D x / dt = ax-bxy-hx = (ah) x-bxy; DY / DT = Cxy-Ey-hy = Cxy- (E h) y}; (4). Compare (4) equation with (1), can be seen exactly the same as that, the former is only converted to AH and E H, respectively, the coefficients of X and Y in (1). . Therefore, the (4) is x '= (∫XDT) / T = (E H) / C, Y' = (∫YYDT) / T = (AH) / B (5). Using (5) We can see: The increase in the attack force H increases X 'to increase Y'. During the exam, because the homework is busy, the pursuit of offensive is reduced, that is, h reduces, compared with the inspection, will be beneficial to the growth of academic performance Y. This is the volterra principle. This principle has an important guiding significance for boys: the powerful love offensive is not necessarily to achieve satisfactory results, but it is unfavorable to grow in the school; sometimes through slow contact, slowly understand, plus appropriate pursuit of action, girls Alienation will slowly decrease. Learning achievements will not be reduced! ! ! ! ! ! ! ! (This article needs to combine "Engineering Mathematical Analysis Basic" Higher Education Publishing Society, Ma Xi En, Wang Miansen, editor - ※ Source:. The Big Green Biggreen.dhs.org. [From: mercury.kiewit.d]
