HQl NGHI KHOA HOC TOAN QUOC V£ SINH THAI VA TAI NGUYEN SINH VAT L A N THLf 5
PHAN TICH MO HINH LOTKA-VOLTERRA V6l PHAN MEM MM & S
NGUYEN VAN SINH Vien Sinh thai vd Tdi nguyen sinh vdi, Vien Hdn lam Khoa hoc vd Cdng nghe Vi^t Nam MM & S la cdng cu md hinh hda va md phdng cac he ddng, da dugc thiet ke tren ca sd quan diem "Bdn nhdm ySu td" va quan diem "He sd bien ddi" (Nguyen Van Sinh, 2006, 2012).
Quan diem "Bon nhdm yeu to" cho rang cac yeu td ciia he dpng cd the chia lam 4 nhdm: (1) Cac y6u td khdng ddi; (2) Cac y6u td trang thai; (3) Cac ygu td trung gian; (4) Cac yeu to liet ke.
Cac yeu td khdng ddi khdng baa gid thay ddi gia tri cua chiing hoac ft nhai la trong thdi gian chung ta xem xet he. Veu td trang thai thay ddi gia tri cua chung nhirng chiing ta cd the xac djnh gia tri cQa chimg d bat cir thdi digm nao bang each can, do, dong, dgm... mac dii ddi khi rat kho. Cac yeu td trung gian thay ddi gia trj ciia chimg va gia tri ciia chiing d mpt thdi diem chi cd the dugc tinh toan tir gia trj ci'ia cac ygu td khac (Bossel, 1992). Va cudi ciing la nhdm yeu td li?t ke, chung thay ddi gia tri theo thdi gian nhung gia trj ciia chiing d mpi thdi diem hay d mot so thdi diem trong khoang thdi gian ta xem xet he da dugc cho trudc (gia trj ciia ehiing dugc liet ke) (Nguyin Van Sinh, 2011).
Quan diem "He sd bien doi" cd nghTa la mdi yeu td trang thai cd mot he sd bien ddi nhu la thupc tinh ciia minh. Cac yeu td khac tac ddng len mpt yeu td trang thai bang viec tac ddng len h? sd bien ddi cua nd va yeu td tr^ng thai tac ddng ten cae yeu td khac ciia h? bang gia tri ciia minh.
Tinh nang gidng nhu phan mem thuang mai Stella ciia My (Bossel, 1992), phan mem MM
& S dugc cung cap mien phi tren trang thdng tin dien tir ciia Vien Sinh thai va Tai nguyen sinh v|t. La cdng cu md hinh hda va md phdng he ddng, phan mem MM & S da dugc ap dung trong vi?c phan tich cac he ddng khac nhau (Nguyen Van Sinh, 2006, 2012; Nguyin Van Sinh vd cpng sir, 2011; Nguyen Hiing Manh vd cgng sir, 2011). Bai bao nay trinh bay viec irng dung MM &S dephan tich md hinh Lotka-Vol terra (Begon Michael vd cgng sic, 1996),
Cdng trinh nay dugc hd trg bdi Vien Han lam Khoa hpc va Cdng nghe Viet Nam, I. VAT LIEU VA PHU'OTVG PHAP NGHIEN CVV
Delphi XE Professional Workstation ESD (so hieu: 2010111885211109) ciia hang Embarcadero da dugc su diing de xay dung phan mem MM & S. Phan mem MM & S dugc su dyngde phan tich md hinh Lotka-Volterra, Phuang phap phan tich he thong, ind hinh hda va mo phong da dugc ap dung (Bossel, 1992).
II. KET QUA VA THAO LUAN I. Nhiin dien ciic yeu to he thong
Md hinh the hien tuang tac ciia hai quan the, Qudn the vgt .san va Qudn the vdi moi. Kich thirdc cua hai quan the thay ddi theo thdi gian. Tuy nhien tai mot thai diem bat ky cd the xac
^inh kich thirdc ciia cac quiin the nay bang each dem cac cd the. Do do, cac quan the nay la yeu lo trang thai Cd mpt gia tri ciia kich thirdc quan the vat mdi khi kich thudc quan the vat san khong thay ddi, dd la Gid trj ddng khuynh vdt sdn. Cung cd mpt gia tri ciia kich thirdc quan thi 1559
HQI NGHI KHOA HQC T O A N Q U O C V £ SINH T H A I V A T A I N G U Y E N SINH VAT L A N THLr 5
vat san khi kich thudc quan the vat mdi khdng thay ddi, dd la Gid trj ddng khuynh vdt moi. Cac gia trj ding khuynh nay la duy nhat cho mpt cap quan the vat san-vat mdi. Vi vgy cac yeu to nay la yeu td khdng ddi. Mdi trudng khdng cho phep kich thudc quan the vat mdi tang vd hgn ma chi dat din mpt kich thudc nhit djnh, gpi la Sire chira vdt mdi. Doi vdi mdi quan the trong moi trudng nhat dinh, gia tri nay la mot gia trj nhat djnh. V) vay day la yeu td khdng ddi. Khi mpt quin the bj xao trpn, kich thudc se thay ddi mpt gia tri nhat dinh, dugc gpi la Dg xdo trgn.
Trong md hinh nay xao trdn la mot thir nghiem tren md hinh va gia trj dp xao trpn dugc d^r kien trudc, vi vay day la mpt yeu to liet ke. Mdi ylu td trang thai cd he sd bien ddi lit thudc tinh cua minh (Nguyen Van Sinh, 2006). Tuy nhien, mpt phan he sd biln ddi ciia quan the viit san ph^i thudc vao quan thi vat mdi, dai Iirgng nay dugc gpi la Phdn thay ddi phu thugc vao vgt mai, no dupe tinh tir kich thudc quan the vat mdi va gia trj dang khuynh vat san. Tirang tu, mot phan h?
sd bien ddi ciia quan thS vat mdi phy thupc vao quan the vat san, dgi Iirgng nay dugc gpi la Phdn thay doi pirn thugc vao vgt sdn. nd dugc tinh tu kich thudc quan the vat san va gia tri ding khuynh vat mdi. Do thay doi theo thdi gian va dugc tinh tir gia trj ciia cac yeu td khac nen cac dai Iugng nay la yeu td trung gian.
Nhu vay he thdng tuang tac cd S yeu td nhu sau: 1/ Quan the vat san (yeu to trang thai);
2/ Quan the vat mdi (yen td trang thai); 3/ Gia tri dang khuynh vai san (yeu td khdng doi); 4/
Gia trj dang khuynh vat moi (yeu td khdng ddi); 5/ Sire chira vat mdi (yeu td khdng doi); 6/ Dp xao trpn (yeu td liet ke), II Phan thay ddi phu thudc vao vat mdi (yeu td trung gian); 8/ Phin thay doi phy thupc vao v^t san (yeu td trung gian),
2. Mo hinh ldi
Md hinh dugc xay dung tren ba gia thilt. Thir nhit, cac quan the se khdng thay ddi kich thudc (sd ca the mat di bang sd ca the sinh ra) trir trudng hgp kich thudc cua quan the v?! m6i khac vdi gia trj dang khuynh vat san hoac kich thudc cua quan the vat san khac vdi gia trj ding khuynh vat moi. Thir hai, mdi trudng cd sire chira nhat djnh cho quan the vgt san. Thir ba, mpt su xao trdn do tac dpng ben ngoai gay ra su tang tire thi kich thudc hai quan the d mpt thdi diem nhit djnh.
Tren ca sd nhan dien yeu td he thdng cac gia thiet tren ta cd the xac dinh cac tuang quan giira cac ylu to nhu sau:
- Phan thay ddi phu thugc vao vat mdi dugc tinh toan tir Gia trj dang khuynh vat sSn va Quan the vat moi;
- He sd bien ddi ciia quan the vat san dugc tinh tir Phan thay doi phu thudc vao,v|it moi va Dp xao trdn;
- Phan thay ddi phu thudc vao vat san dugc tinh tir Gia trj dang khuynh vat mdi va Quan the vat san;
- He sd bien ddi ciia quan the vat mdi dugc tinh tir Phan thay ddi phu thudc vao v^t san vao Dp xao trpn va Sire chira vat mdi.
3. Sff do md phong
Dua tren md hinh ldi, sa dd mo phdng dugc xay dung nhu tren hinh I. Bang viec sir diing4 bieu tugng dai dien cho cac yeu td ciia 4 nhdm ylu td (hinh vudng cho ylu td tr^ng thai, hinh thoi cho yeu td trung gian, hinh trdn cd cac diu cpng/trir ben trong cho yeu td Met ke va hlnn trdn trdng cho ylu t6 khong doi) phin mem MM & S cho ta thiy ban chat toan hgc ciia m6i yeu td tren sa dd.
HQI NGHI KHOA HQC T O A N O U O C V £ SINH THAI V A TAI NGUYgN SINH V A T L ^ N THlj 5
Cda sd con T^p Md hinh d^ng van b ^ Delhi So ddmfi phdng Bing Thiichiln Trai
Blal |,.| lA|i-lsl,sl».1r;|tt| lal..|»|ir:J.ll
^ Su na mO phdng - lolka-voHera.vec
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Gia trj dang khuynh %al san
Phil thay it'i rfiy Ihugc \ko vgt m5i , / ^ ^ . ^ ' & ^ x
Quan the vai san ^ - ^ ^ otrpn
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^ . ^ , _ ; __.A^J-m^M
[ \ Siic chiia vgt mdi ' 1 Quan Ihe vai moi , 1
^^Phan thay ddi phu thuoc vao vat san
\ ^ Gia tri dSng khuynh v^t moi
_
Hinh I. Sa do md phong ciia md hinh Lolka- Vo!terra 4. Luo'ng hoa cue yeu to he thong vii viet md hinh toan
Mdi yeu td dugc dai dien trong md hinh bdi mpt bien. De lam cho md hinh de hieu, ten bien dugc tao ra tir ten yeu td vdi viec bd dau each. De lugng hda va thuc hien tinh toan md phong trirdc het can xac djnh budc thdi gian. Trong md hinh nay budc thdi gian la 1 nam vi cac he so bien ddi ciia cac yeu td trang thai (Quan the vat san, Quan the vat mdi) cd co sd la nam. Day la md hinh iy thuyet, vi vay phuang phap Iugng hda luang ddi dugc ap dung (gia tri ban dau cua cac yeu td trang thai bang I ) , Gia trj ciia cac yeu td khdng ddi dugc udc lupng nhu sau: Gia trj dang khuynh vat san = 2. Gia trj dang khuynh vat mdi = 2, Sue chira vat mdi
= 2. Yeu td Dp xao trpn (yeu td liet ke) cd gia trj 0 d thdi diem 300 khi thirc hien tinh loan md phong binh thudng (khdng cd xao trdn xay ra) va dugc nhan gia trj khac 0 khi thuc hien thir nghiem tren md hinh.
Khi quan the vat moi ldn hon gia trj dang khuynh \ a t san, quan the vat san se cd ca hpi ldn han de bat dugc vat mdi, dieu dd cd nghTa la dieu kien cho sinh san cung tdt hon va ngugc lai.
Cung vay, khi quan the vat san nhd hon gia trj dang khuynh vat mdi, ca hpi song sdt ciia vat moi tdt hon va ngugc lai. V i the, cac cdng thuc de tinh toan cac yeu td trung gian dugc udc Iirgng nhu sau:
phanthayddiphythudcvaovatmdi = 0.03* (quanthevalnidi-giatridangkluiynhvalsan) phanthaydoiphiithupcvaovatsan = 0.03* (giatrjdangkhuynhvatmoi-quanthevalsan) Quan the vat san thay ddi kich thudc phu thupc vao Phan thay ddi phu thudc vao vat m6i va Dp xao trpn. V i vay cdng thirc tinh he sd bien ddi ciia Quan the vat san nlur sau:
biendong_quanthev(itsan = phanthaydoiphuthupcvaovatnidi+Dpxaotrpn
Ngoai tac dpng ciia Quan the vat san va Dp xao trdn, tang trirdng ciia Quan the vat mdi cung phu thupc vao Sire chira vat mdi ciia mdi tnrdng Quan the vat moi cang ldn ho'n Sire chira vjt moi. ap lire mdi trudng len su tang trudng ciia nd cang ldn, V i vay cdng thirc tinh he so b i l n doi ciia Quan the vat nidi nhu sau:
HQl NGH! KHOA HQC T O A N Q U O C V £ SINH THAI VA TAI NGUYEN SINH VAT L A N T H l j 5 biendongquinthevatmdi = if (quinthevatmdi> succhuavatmdi)
then (Dd.\aotrpn+phinthayddiphulhugcv4ovatsan-0.015* (quanthevatmdi-sircchiravalmcii)) else(Ddxaotrgn+phanthayddiphuthupcvaovatsan)
Trong MM & S, cdng thuc chung de tinh bien trang thai nhu sau:
StateVariable (t) = State_Variable (t-dt)+Change_Rate (dt) 5. Nap md hinh vao sa do mo phdng
De nap md hinh vao sa do md phdng, ta kich diip chugt len tirng bieu tugng sau do njip thdng lin va cong thirc vao hop thoai hien ra (hinh 2),
Thang tin v&ygu tottgng thai i<»i.wiw..wM<uw,.«M4w^S8w»M4MWtfc-^' G j ^ j l
Ten biin tnmg a j l " * » * " ' ' » ^ '
Gia tri ban d^l ^ S i thii ti^p iCong thiic tinh bien d^ng ciia bien trang thai:
i f( quanthe\~atm6 i>succhiiavalm5 i)lhen(D6xaotr9n+phantbaydd ip , | . | - | - | , ^ d | . , | . .
" |n~|a-l (
• l ' h l = l<
)
5<
6>
7A
M M HamsB;Abs Arccos :=|
Arcs in Bl tac don^ boi c^c yeu to:
phanthaydo iphuthupc vao valsan D9xaotr9a[D9 xao tr^n]
siicchiiavatm6i[Sin: chua v^t n
Tde dgng len cic yeu tfl:
phanthaydo iph^thu c
Hinh 2. Hop thoai nap thong tin cho yeu td trong sa do mo phdng
Sau khi nap md hinh vao sa do md phdng, ta can cho MM & S kiem tra tinh hoan thien cua so dd trudc khi tinh toan md hinh hoac xuat mo hinh ra tep van ban, de thuc hi?n viec do ta kich chudt len nut kiem tra tren thanh cdng cu ciia cira sd sa do md phdng (bang I).
Chirc nang cua cac nut cdng cu chinh Nut
• / e.l'
J ^
Chirc nang Kiem tra tinh ho^n thien cua sa do mo phong Xuat mo hinh tip so do mo phong ra tpp van ban
Niit Ipnh chay mo hinh: Ch^y mo hinh trong tep van ban (nut tren thanh cong cy cda so chinh) hoac chay md hinh trong sa d6 mo phong (niit tren thanh cong cy cda so so d6 mo phdng)
^ HQI NGH] KHOA HQC TQAN QUOC VE SINH THAI VA TAI NGUYEN SINH VAT L A N THlJ 5 6. Mo hinh dang van ban
Khi sa do md phdng da hoan thien, ta cd the xuat md hinh ra tep van ban. Dl thuc hi?n viec dd ta kich chudt len mit xuat md hinh (bang I), dat ten tep va nap khung thdi gian cho md hinh qua cac hpp thoai hien ra. Ket qua ta se cd md hinh dang van ban dugc luu trong tep nhu dudi day:
[*]STARTTIME=0 [*]ENDTIME=900 [*]TIMESTEP=1 CONSTANT_ELEMENTS
[*]giatridangkhuynhvatsan=2 [*]giatridangkhuynhvatmdi=2 [*]succhuavatmdi=2 LISTEDELEMENTS
[ * ] Ddxaotrdn=/—/3 00=0 INTERMEDIATE_ELEMENTS
[*]phanthayddiphuthupcvaovatmdi=0,03* (quanlhevatmdi-giatrjdingkhuynhvatsan) [*lphanthayddiphuthupcvaovatsan=0.03* (giatrjdingkhuynhvatmdi-quinthlvatsan) STATE_ELEMENTS
[*]quanthevatsan=l
[**]biendong_quanlhev9tsan=phanthayddiphiithugcvaovatmdi+Dpxaotrpn [*]quanthevatmdi=I
[**]biendong_quanthev§tmdi=if (quanthevatmdi> succhiravatmdi)then (Ddxaolrpii+
phanthayddiphuthiipcvaovatsan-0.015* (quanthev?tmdi-succhuavatmdi))else (Dpxaotrpn+phan thaydoiphuthupcvaovatsan)
7. Chay mo hinh ftCOasdWng^KA 0 Bu0c tinl Bieu thiic Gid tri ba 1 2 3 4 3 6 7 8 9 10 11
1 Tlidi pi 0 0 2 3 4 5 6 7 3 9 to 11
qua.tbl^
2 quanihe 1 1
3 biendoi phanCha -0,03
4 quanthe 1 1
5 biendoi if(quiil 0,03
6 phantha 0 03*(q -0,03
7 phan tha 0 . 0 3 ' ( E 0,03
8 eiatridl 2 2
9 Btatrida 2 2 0,97 -0,0291,1,03 0,0309 I-O,029l0,0309 2 2 0,94'09 1-0,0282,1,0609 ,0,0318 -0,0382|0,6318 ,2 '.2 0,9127 -0,0272 1,0927 ,0,0326 :-0,0272 0,0326 2 2 0,8855 ;-0,0262 1,1253 o",033"4 |-0,02620,0334 2 ' 2 0,8593 ^-0,0252'1,1587 0,0342 1-0,0252,0,0342 2 2 0,8341-0,0242 1,1929 0,035 1-0,0242 0,035 2 2 0,8099 |-0,0232 1,2279 0,0357 [-b,023l|0i0377~ ,2 """"'2 0,7867 -0,0221 1,2636 |o,0364'-0,02210,0364 2 2 0,7646 1-0,021 .1,3 _ 10^0371_j-0,021 '0,0371 2 2 0,7436 1-0,01991,3371 10,037^1-0,0199 0,0377 2 2 0.7237 -0.0188 1.3748 0.0383 -0.0188 0.0383 2 2
•-1^
10 siicchlir 2 2 2 2 2 2 2 2 2 2 2 2"
l-Q-warf u 1-
DoxaotJ^
/—/3oq 0 1 0 0 0 0 0 0 0 0 0 0 " _ 0 LTinh 3. Cira .\6 bdng vd kel qua linh loan md phdng ciia md hmh
HQl NGHI KHOA HQC T O A N Q U O C V £ SINH T H A I V A T A I N G U Y £ N SINH VAT L A N THLf 5
D I chay md hinh trong cira sd so dd md phdng dang md, ta ki'ch chupt len niit lenh chay mo hinh tren thanh cdng cu cua cira sd nay va nap khung thdi gian cho md hinh. D I chay mo hinh dugc luu trong tep van ban, ta kich chudt len niit lenh chay md hinh tren thanh cdng c^ ciia cira sd chinh va chgn tep md hinh trong hgp thoai md ra.
Sau khi chay md hinh, MM & S se hiln thi ket qua tinh toan md phdng trong mpt cira sd bang (hinh 3). Chay md hinh khdng cd xao Iron va cd xao trpn (Ddxaotrdn = I d thdi diem 300) va sau dd ve cac dd thi thdi gian va dd thi pha, chung ta se cd ket qua nhu trong cac hinh 3-6. Trong dd thi pha, diem dau dugc danh dau bang dau cgng va dilm cudi dupe danh dau bangsd 1.
Nhu cd the thay tren cac dd thi d hinh 4 va 5, cac gia tri ban dau ciia cac yeu Id trang ihaj khdng tuang irng vdi trang thai can bang ciia he. Tuy nhien, he thdng cd xu hudng dat tdi trgng thai can bang (hinh 4, 5).
Hmh 4. Dd thi thdi gian (khdng cd xdo trgn)
0 5689,1 OiOO i]uiatlierilmgj(3 0193)
Hinh 5. Do thj pha (khdng cd xdo trgn)
8. ThiJr nghiem gay xao trpn cho he thong
De thii nghiem gay xao trpn cho h? thdng, gia trj ciia yeu td lipt ke Dp xao trpn d thdi diem 300 dugc dat la 1. Tren thyc te day cd the la ket qua ciia viec tha them ca vgt s5n va v?t nu6i vao mdi trudng. Trong trudng hgp cd sir xao trgn (hinh 6, 7), h$ thdng bj day ngugc I^i ra xa trang thai can bang. Tuy nhien, he thdng vin cd xu hudng dat tdi trang thai can bing.
Tiep theo thir nghiem dugc thuc hien cho trudng hgp, khi cac chu trinh ciia quan the vat s5n va quan the vat mdi da d trang thai dn djnh. De thirc hifn vifc dd, Dg xao trpn dugc gan cho gia trj bang 1 tai thdi diem 6000 va md hinh dugc chay vdi khung thdi gian tir 0 den 9000. D6 thj thdi gian ciia ket qua tinh toan md phdng dugc trinh bay d hinh 8.
Theo Begon Michael, John L. Harper, Colin R. Townsend (1996) (chuang 10, trang 300), cap chu trinh ciia cac quan the vat san va vat mdi the hien tfnh on djnh trung lap: Chimg tiep tyc vd han neu khdng bj xao trdn, nhung mdi sir xao trdn den mpt dp phong phii mdi se bat dau mpt loat cac chu trinh on djnh mdi, khac, xung quanh cac gia trj trung binh cu nhung vdi bien dp khac. Trong thir nghiem d day, nhu dugc th^ hien rd tren hinh 8, sau khi xay ra xao trgn va d?t den mgt dp phong phii mdi, cap chu trinh van trd lai on dinh vdi bien dp nhu trirdc khi xay ra xao trpn.
HQI NGHI KHOA HOC TOAN QUOC V£ SINH THAI VATAI NGUYEN SINH VAT LAN T H l j 5
•1 -i]i.anili<.3'."iiC'' '
Hmh 6. Dd thi thdi gian (Do xdo trdn = 1 a thai diem 300)
Hmh 7. Do thi pha (Dg xdo trgn = 1 d thdi diem 300)
iL ^ - I C I -
-:Cr>quantlievali5n- Il ?69---'3 JJS
Hmh S. Do thi thai gian ket qua md phdng co xdo Iron (Do xdo trgn = 1 a thai dUm 6000) 9. Phiin tich do nhay
Vi?c phan tich do nhgy dugc thuc hien de hieu viec gia tri mpt tham sd he thong (gia trj bgn dau cda cac yeu td trang thai, hoac gia trj ciia cac yeu td khdng ddi) thay ddi se anh hudng den ddng thai cua he thong nhir the nao. 0 day, gia tri ciia Sire chira vat mdi dugc thay ddi va xem xet sir anh hudng ctia thay ddi nay den ddng thai ciia cac quan the vat san va vat moi. Lira chpn thuc hien phan tich dp nhay dugc chuyen dat la cd (hinh 9). Sau dd cac yeu td dugc chgn de ve dd thi thdi gian.
Dd i>u ihtn gian 1 F>a dii phj Ph^
quantlic\ alson qudIlthu^ ^tni6i f !3li|ilaiigkliuynhl jtsan eialriJ^i^iuynhv^tiiioi
1 Tlnicbtn uch do nhj y
-> |si>cchlia\^Unai Tiiii^ h r i d . h
4 5 a
Tliuc hjcn ptiia uch dg flh:
IS C<5 r Khflog
11 T^U 1 Hinh 9. Dgt gid tri de phdn lich do nhay
HQI NGHI KHOA HQC T O A N Q U O C V £ SINH T H A I V A TAI N G U Y E N SINH VAT L A N THCf 5 Vdi mdi gia tri ciia sire chira vat nidi, MM & S thuc hien tinh toan md phdng va sir dyng kk qua d^ ve dd thj (hinh 10), Cac dd thj lien tiep dugc thay thi the hien mgt each hinh tupng dp nhay ciia cac yeu to vdi su thay ddi gia trj ciia tham sd Sue chira vat mdi.
Nhu dugc the hien tren hinh 10, ddng thai ciia cac quan the vat san va vat mdi nhay cam vdi su thay ddi gia trj cua tham sd Sue chua vat mdi. Vdi cac gia trj hien thdi ciia cac yeu ti khac, mot gia tri nhd hon 3 ciia Sire chiia vat moi se dam bao xu the dat dugc su can bang va mgt gia tri ldn hem 3 ciia Sire chua vat mdi se dan den xu the tang dan bien do dao ddng cac quan the vat san va vat moi.
siicchiia\ atnio i=1.9 siicchiiav5lm6i=3,1 siJcchirav9tm6i=3,9
-Buac linh loan- 900 -Buac tinh loan- 900 -Eiroc tinh loan- Hinh 10. Do thi thdi gian vdi cdc gid tri khde nhau ciia Sire chira vdi moi
III. KET LUAN
Mpt phien ban md hinh Lotka-Volterra da dugc xay dung cho phan mem MM & S (Mo hinh hoa va md phdng he thdng). Md hinh bao gdin 8 yeu td he thong: Hai yeu to trang thai (Quan the vat san, Quan the vat mdi), ba yeu td khdng ddi (Gia tri dang khuynh vat san, Gia trj dang khuynh vat moi. Sire chira vat mdi), mgt yeu td liet ke (Dp xao trpn), hai yeu to trung gian (Phan thay ddi phu thupc vao vat moi, Phan thay ddi phu thugc vao vat san).
Ket qua tinh toan md phdng cho thay gia trj ban dau ciia cac yeu to trang thai khdng tuong irng vdi trang thai can bang cua he thdng. Tuy nhien, he thdng cd xu hudng dat tdi trang thai can bang vdi thdi gian.
Begon Michael, John L. Harper, Colin R Townsend (1996) khang djnh ring cap chu trinh cua cac quan the vat san va vat moi the hien tinh dn dinh trung lap: Chiing tiep tuc vd han neu khdng bj xao trgn, nhung mdi su xao trgn den mgt do phong phii mdi se bat dau mpt loat cac chu trinh dn djnh mdi, khac, xung quanh cac gia tri trung binh cu nhung vdi bien dp khac. Tuy nhien, ket qua phan tich md hinh d day cho thay, trong trudng hgp cd sir xao trgn dan den dp phong phii mdi ciia cac quin the, he thong bi dua ra khdi trang thai can bing nhung sau do c?p chu trinh van trd lai dn dinh vdi bien dp nhu triroc khi xay ra xao trgn.
Ket qua phan tich do nhay cho thay, vdi cac gia tri hien thdi ciia cac y6u to khac, dpng thai ciia cac quan the vat san va vat mdi nhay cam vdi Sire chira vat moi.
TAI LIEU THAM KHAO
I Begon Michael, John L. Harper, Colin R. Townsend, 1996. Ecology: individuals, populations and communities. Blackwell Science Ltd. ISBN 0-632-03801-2 (pbk), ISBN 0-86542-845-X (hbk).
2. Bossel H., 1992. Modellbiidung und Simulation. Friedr. Vieweg & Sohn Veriagsgesellschaft mbH:
Braunschweig/Wiesbaden, Deutschland (German).
1566
HQl NGHI KHOA HOC T O A N Q U O C V £ SINH THAI VA T A I NGUYEN SINH VAT 1-AN T H Q 5 3. http://iebr.ac.vn/pages/emms.asp. Trang thdng tin dien tir phan mem MM & S. Ngay tiip can:
12/07/2013.
^. http://www.embarcadero.com: Trang thong tin dien tu cua cong ty Embarcadero. Ngay ti^p can:
12/05/2013.
5, International Society for Ecological Economics, 2004. Software reference guide: STELLA software technical documentation. ISEE Systems.
6, Nguyen Hung M^inh, Nguyen V3n Sinh, Nguyen Manh Hiing, 2011. Bao cao Khoa hpc ve Sinh th^i va Tai nguyen sinh vat, Hpi nghj Khoa hpc toan qu6c lan thii tu, H^ Npi, 21/10/2011, tr. 1706- 1712 (ISSN 1859-4425).
7, Nguyin Van Sinh, 2005. Phan tich he thong, mo hinh hoa va mo phong vdi ph^n mfim MM & S, TuyIn tap Bao cao Khoa hpc Hdi nghi moi trudng toan quoc, 21-22/4/2005, Ha Noi, tr. 1347-1358.
8 Nguyen Van Sinh, 2006. An effort to enhance the computer simulation of dynamic systems: an example with mini-world model. Proceeding of the lUFRO international conference: 'PATTERNS AND PROCESSES IN FOREST LANDSCAPES-Consequences of human management'. 26-29 September 2006, Bari, Italy (ISBN-10: 88-87553-11-4; lSBN-13: 978-88-87553-11-6). p.: 543-549, 9. Nguyen Van Sinh, 2011: Bio cao Khoa hpc ve Sinh thai va Tai nguyen sinh vat, Hpi nghj Khoa hpc
t o a n q u 6 c i a n t h u t u , Ha Npi, 21/10/201 l,tr. 1778-1783.
10. Nguyen Van Sinh, Nguyen Hiing Mfinh, Nguyen Manh Hung, 2011. Bao cao Khoa hpc ve Sinh thai v^ Tai nguyen sinh vat, Hpi nghj Khoa hpc toan qu6c l^nthirtu, Ha Npi, 21/10/2011, tr. 1784-1791.
il. Nguyen Van Sinh, 2012. The Change Rate Concepts and their Realization in the MM & S-a Computer Program for Modeling and Simulation of Dynamic Systems. Lecture Notes in Electrical Engineering, Vol. 152: 1-13, Springer (ISSN: 1876-1100; ISBN: 978-1-4614-3534-1).
ANALYSIS OF THE LOTKA-VOLTERRA MODEL WITH MM & S SOFTWARE NGUYEN VAN SINH
SUMMARY
The paper presents the analysis ofthe Lotka-Volterra model with MM & S software. This software is designed based on the "Four Element Groups Concept" as well as on the "Change Rate Concept" and has been applied for analysis of different dynamic systems. A version of Lolka-Volterra model has been developed that includes 8 system elements- Two stale elements (Predator populat'on, Prey population), three constant elements (Predator zero isocline, Prey zero isocline, Prey capacity}, one listed element (Disturbance), two intermediate elements (Prey related change of predator population. Predator related change of prey population) The simulation calculation has shown that in the case of a disturbance the system is putting backward from equylibnum but still tends to achieve equylibnum after that Begon Michael. John L Harper, Colin R. Townsend (1996) slated, that "the coupled cycles of predator and prey populations exhibit neutral stability; They continue indefinitely if undisturbed, but each disturbance to a new abundance initiates a new, different series of neutrally stable cycles, around the same means but with a different amplitude" However, our investigations have shown that after a disturbance to a new abundance, the coupled cycles will become stable later with the same amplitude as before disturbance.
The sensiUvity analysis has shown that the dynamics of Predator and Prey populations are sensitive to changing value of Prey capacity.
