Frog Call-Inspired Self-Organizing Anti-Phase Synchronization for Wireless Sensor Networks

Transcription

1 Frog Call-Inspred Self-Organzng Ant-Phase Synchronzaton for Wreless Sensor Networks Akra Mutazono Graduate School of Informaton Scence and Technology Osaka Unversty -5, Yamadaoka, Suta-sh, Osaka , Japan Emal: Masash Sugano School of Comprehensve Rehabltaton Osaka Prefecture Unversty 3-7-3, Habkno, Habkno-sh, Osaka, , Japan Emal: Masayuk Murata Graduate School of Informaton Scence and Technology Osaka Unversty -5, Yamadaoka, Suta-sh, Osaka , Japan Emal: Abstract In ths paper, we focus on the callng behavor of Japanese tree frogs, whch make calls alternately wth ther neghbors n order to ncrease the probablty of matng. Ths behavor can be appled n phase control whch realzes collsonfree transmsson schedulng n wreless communcaton. We propose a self-organzng schedulng scheme nspred by ths frog callng behavor for relable data transmsson n wreless sensor networks. Smulaton results show that our proposed method for phase control s capable of reducng data transmsson falures and mproves the data collecton rato up to 24 % compared to a random transmsson method. I. INTRODUCTION Self-organzed control nspred by bologcal systems has been recevng more attenton as a concept for the realzaton of hgh robustness, scalablty, and adaptablty []. Each component of a bologcal system makes decsons based on local nteractons wth ts neghbors, wthout recevng drectons from a specfc leader. Thus, the entre system can respond to changes n a coordnated manner n spte of the self-orented behavor of the ndvdual components. Such smple mechansms brng cogntve functonalty to the whole system, and self-organzed control provdes adaptablty and robustness [2]. There has been methods proposed to adopt the advantages of bologcal systems to computer networks n such felds as routng [3] and clusterng [4]. In the feld of tme synchronzaton, pulse-coupled oscllators (PCO) [5] are known to model the behavor of frefles, whch flash n unson wth ther neghbors. However, most research on the pulse-coupled oscllator model has focused on smultaneous synchronzaton [6]. Antphase synchronzaton [7] (alternate phase synchronzaton) s necessary n the case where several termnals need to share common resources. When several termnals process a task by sharng common resources, the load can be balanced by applyng round-robn schedulng, where each termnal s processed n turns. Smlarly, n wreless communcaton, ant-phase synchronzaton of transmsson schedulng reduces packet loss caused by collsons. As a possble mechansm for realzng ant-phase synchronzaton, we consder the callng behavor of Japanese tree frogs [8], especally advertsement callng. It s consdered that Fg.. Japanese tree frog (Hyla japonca). one of the man reasons for the callng behavor of ths type of frog s to attract females. If a male calls smultaneously wth other frogs, t becomes dffcult for the female to dstngush the caller, and therefore they shft the tmng of ther calls [9, ]. We formulate ths behavor of advertsement callng by usng the pulse-coupled oscllator model, and t s appled n phase control for ant-phase synchronzaton as well as n transmsson schedulng n wreless communcaton wth the am of avodng transmsson falures. Conventonal schedulng protocols have problems regardng the overhead for adjustng ther schedule and lack n adaptablty snce the schedule s fxed and cannot be rescheduled n accordance wth envronmental changes. However, self-organzng schedulng based on frog callng s expected to solve these problems. In ths paper, we propose a self-organzng transmsson schedulng scheme nspred by frog callng behavor. We demonstrate that phase control can result n ant-phase synchronzaton n varous envronments, and we perform a comparatve evaluaton wth DESYNC [, 2], whch s another dstrbuted ant-phase synchronzaton technque. The outlne of ths paper s as follows: Secton II provdes the motvaton and some related work about ant-phase synchronzaton. Secton III ntroduces detals of the mechansms of the phase control method based on frogs alternate callng behavor. Secton IV shows the result from numercal smu-

2 callng slot B A C collson collson phase control Fg. 2. Hdden termnal problem. Termnal B and C may transmt smultaneously n order not to know a mutual exstence. latons n sngle-hop networks. We provde a concluson and present possble extensons n Secton V. II. ALTERNATE PHASE SYNCHRONIZATION FOR SCHEDULING Research on tme synchronzaton usng pulse-coupled oscllator model has been performed [3]. Those work target at adjustng oscllators phase n unson, however the research on synchronzaton that shfts the phase of oscllators wth certan ntervals has not been prevously consdered n detal. We call conventonal smultaneous synchronzaton as nphase synchronzaton and call alternate synchronzaton of our target as ant-phase synchronzaton. For nstance, n-phase synchronzaton s the phenomenon of smultaneous flashng of frefles and ant-phase synchronzaton s seen n Chrstmas llumnatons where the colorful bulbs flash alternately or alternate blnkng of the crossng lamp. Ant-phase synchronzaton becomes effectve for sharng the resource. Round-robn schedulng s known whch assgns the same tme slce to the process of a watng state n order wthout prorty. Ths method s supposed to be far schedulng snce resource s allocated to all the processes equally. In the feld of wreless communcaton, TDMA (Tme Dvson Multple Access) s also a knd of ant-phase synchronzaton whch dvdes the access perod nto fxed slots and assgns frequency used for communcaton. In TDMA, snce t s not necessary to check a channel, delay s small and stable transmsson speed s expectable. Furthermore, f ant-phase synchronzaton s appled to mult-hop network, a collson n the MAC layer n the wreless sensor network s avodable. We explan the hdden termnal problem as a example of collson n MAC layer usng Fgure 2. When termnal B communcates to termnal A, collsons do not occur because termnal B checks the channel s free (carrer sense) before transmsson. However, when termnal C s added here, termnal B and C can not check the channel properly snce they are located out of communcaton range each other. In such case, when two termnals transmt smultaneously, nterference takes place at the pont of termnal A and the packet does not reach termnal A correctly. Ths s the hdden termnal problem whch can be serous problems n wreless sensor networks. Interference can be reduced f the termnals n the relaton of hdden termnal problem adjust transmsson schedule by ant-phase synchronzaton. Fg. 3. Outlne of phase control whch reduces the transmsson falure by adjustng the transmsson tmng. There are some studes about ant-phase synchronzaton. DESYNC [, 2] s a ant-phase synchronzaton method n dstrbuted manner proposed by Nagpal et al.. Each node adjusts the frng tme consderng the last and next frng of tself so that the offsets of frngs become equal. Even when there are many nodes, teraton of nteractons leads whole network to ant-phase synchronzed state. But, adjustment of tmng n ths method reles on nformaton from only two nodes, ths structure s not effectve to mult-hop network. Stankovc [4] proposed another ant-phase synchronzaton method. Ths method adjusts the frng tme for rare event detecton consderng the dstrbuton of sensng regon. However, ths method needs a lot of calculaton resources for buldng complex polynomal functon and locaton nformaton of the neghborng nodes s necessary for accurate ant-phase synchronzaton. PDTD (Phase Dffuson Tme Dvson) [5] s a knd of ant-phase synchronzaton method that performs n a self-organzng manner. Ths method solves the hdden termnal problem by performng ant-phase synchronzaton between nodes wthn nteracton range whch s twce as large as communcaton range. III. TRANSMISSION SCHEDULING INSPIRED BY FROG CALLING The outlne of phase control s shown n Fgure 3. The frog calls by makng a sound for a certan perod of tme and then quets down before repeatng the call. If two or more male frogs call at random, the tmng of ther calls mght overlap. In such a case, the calls nterfere wth each other and the female frog (the matng partner) cannot dstngush between the callers. Therefore, each male frog shfts the tmng of ts calls by lstenng to the calls of other frogs so as to avod such overlap. After all frogs establsh ths nteracton pattern, call alternaton wthout nterference s acheved wthn the group. Pulse-coupled oscllators are used as models of varous synchronzaton mechansms n bology. Here, we formulate frog callng behavor wth pulse-coupled oscllators. Each oscllator has a phase φ [, 2π] whch changes wth tme wth a frng frequency ω. When the phase reaches 2π, the oscllator fres and returns the phase to the ntal value (φ =). Oscllator j whch s coupled wth frng oscllator receves a stmulus and changes the frng frequency of the next turn n accordance

3 š k š«š k Fre j š š š«š k + < š k + = Fre š«fre j šj k š + šjk > š š + k šk k šk«šj j š«+ š + (a) (b) (c) Fg. 4. Phase control mechansm. (a) Each oscllator has ts own phase and frng frequency. (b) Oscllator receves postve stmulus and promote frng frequency, oscllator k receves negatve stmulus and repress the frng frequency. (c) After teratons, the phase offset between each oscllator becomes equal and ant-phase synchronzaton s realzed. wth the phase offset Δ j [, 2π] between the coupled oscllators. The oscllator does not change the frng frequency mmedately after recevng the stmulus; nstead, t memorzes the sze of the stmulus and changes the frng frequency after frng ts own stmulus. ω j = dφ j dt () Δ j = φ j φ (2) ω + j = ω j + g(δ j ) (3) where g() s the phase shft functon whch generates repulsve force whch shfts the phase away from that of other oscllators. Ahara et al. [6] suggested the followng phase shft functon: g(δ) = α sn Δ (4) where α>s the couplng coeffcent of a pulse-coupled oscllator model. When Δ j < π, then g(δ j ) > and oscllator j advances the frng frequency to extend the phase offset wth respect to oscllator. On the contrary, when Δ j > π, then g(δ j ) < and oscllator j slows down the frng frequency n order to spread the phase offset wth respect to oscllator. After these nteractons, the oscllators are assumed to be n a stable ant-phase synchronzed state when the followng condtons of Eqs. (5) and (6) are fulflled (Fgure 4). Δ j =Δ j (5) g(δ j )=g(δ j )= (6) We then consder the group N, nwhchn oscllators are coupled wth each other. When oscllator j fres at tme t j (t <t 2 < <t n ), t changes the frng frequency ω j as follows: Δ j = φ j (t ) φ j (t ) (7) ω + j = ω + g(δ jk ) (8) k N (a) (b) (c) (d) Fg. 5. Dffculty on ant-phase synchronzaton. More than four oscllators are dvded nto the group of two oscllators and the group of three oscllators, they are ant-phase synchronzed n each group. When the phase offsets between oscllators whch fre consstently are all equal and the repulsve force of all oscllators s negated, the group s assumed to be n a stable ant-phase synchronzed state. These condtons are descrbed below together wth the case of two oscllators. Δ 2 =Δ 23 =... =Δ n (9) g(δ k )= g(δ 2k )=... = g(δ nk ) () k N k N k N It s confrmed that two or three oscllators can be ant-phase synchronzed wth phase shft functon Eq. (4) (Fgure 5(a), (b)). However, ths functon cannot ant-phase synchronze more than four oscllators snce they are dvded nto groups of two and three oscllators (Fgure 5(c), (d)). Ths s caused by the phase shft functon, whch s a symmetrc functon, and the repulsve force s negated n stuatons n whch condton Eq. (9) s not satsfed, despte the fact that condton Eq. () s satsfed and the oscllators converge to a stable state. The stmulus needs to be weghted dependng on the phase dstance δ n order to resolve ths problem. The smaller the phase dstance δ between the coupled oscllators, the stronger the oscllators should be n order to receve the stmulus. For ths reason, we adopt the followng equaton. δ(δ) = mn{δ, 2π Δ} () g(δ) = α sn(δ) exp( δ(δ)) (2)

4 Relatve Phase Offset Lower Bound of nodes nodes 5 nodes Couplng Coeffcent ( α) Fg. 6. Transson of relatve phase offset. (a) Relaton between couplng coeffcent α and lower bound of average error. By usng ths phase shft functon Eq. (2), condtons (9) and () are always satsfed, regardless of the number of oscllators. Fgure 6 shows the process of ant-phase synchronzaton between oscllators. The phase of the oscllators, whch s dscrete n the ntal state, s shfted to an antphase synchronzed state wth nteractons between coupled oscllators. The phase offset between consecutve oscllators becomes approxmately the same at tme =. second. After ths pont, although the oscllator receves stmul, postve and negatve stmul cancel each other out, and the group mantans a stable state. IV. EVALUATION A. Smulaton setup Through smulatons, sensor nodes are deployed randomly n a montorng regon wth a radus of m and the tmng of data transmsson s determned on the bass of a phase whch s assgned randomly n the ntal state. The communcaton range of the node s assumed to be 2 m, and the nodes can communcate wth all other nodes n the network. The node carres out sensng every.6 seconds and transmts the sensed data to the snk node at a transmsson speed of 5 kbps. CSMA/CA s used for the transmsson protocol of the MAC layer. Data packets nclude the sensng nformaton and a tme stamp, whch represents the delay caused by the back-off of CSMA/CA. The sze of the packet s set to 4 bts. Therefore, t takes 8 ms for transmttng one data packet, and the transmsson node takes exclusve control of the communcaton band durng that perod. We use the followng evaluaton metrcs. Ths value shows the average value of the phase offset between nodes. The smaller the average error, the hgher the accuracy of the synchronzaton. Transmsson Falure Probablty The probablty of transmsson falure caused by overfalure of the back-off n CSMA/CA durng the commu α =. α =. α = (b) Transton of average error wth nodes. Fg. 7. Settng of couplng coeffcent α. ncaton attempt of the node. Data Collecton Rato Rato of the number of data packets reachng the snk to the overall number of data packets sent to the snk from the node. B. Performance of the proposed phase control mechansm We evaluate the couplng coeffcent α, whch s an mportant parameter of the pulse-coupled oscllator model. In order to obtan the sutable parameter settngs n accordance wth the number of nodes, we estmate the average error after a certan perod (2 seconds). Fgure 7(a) shows that the average error of 2 becomes the boundary value for synchronzaton, where the accuracy of synchronzaton becomes hgher wth tme f t s lower than the boundary value, otherwse the phase keeps fluctuatng and does not converge to a stable state. Addtonally, the large wdth of the couplng coeffcent

5 enables the network to reach a stable state n envronments consstng of a small number of nodes, and t becomes dffcult to converge to the stable state f the value of the couplng coeffcent s too large. Ths s a result of the number of coupled nodes, n other words, the stmulus becomes stronger as the node becomes coupled wth more nodes and the couplng coeffcent becomes larger. Hence, t s concluded from the smulaton that overstmulaton dsturbs the convergence to a stable state. On the contrary, although small values of the couplng coeffcent requre longer synchronzaton tmes, the condton approaches a stable state n a steady manner (Fgure 7(b)). These results ndcate that ant-phase synchronzaton requres the couplng coeffcent to be set adaptvely. The choce of couplng coeffcent also depends on the requrements of the partcular applcaton; for example, a small couplng coeffcent for delay-tolerant applcatons and large couplng coeffcent for accuracy-tolerant applcaton. The number of nodes and the data transmsson nterval also affects the choce. Varous factors should be consdered when settng the couplng coeffcent, and t s assumed that those factors constantly change. Therefore, settng a statc couplng coeffcent s not suffcent, and t s requred that the parameter s set dynamcally for each node n accordance wth the number of nodes and the amount of traffc n a self-organzng manner. However, as ths problem s beyond the scope of ths work, t wll be left for future study. The phase control method requres scalablty over the number of nodes. We perform an evaluaton of a network where 4, or 2 nodes are deployed, and use a couplng coeffcent of.6 n all three cases. The result of the average error wth the progress of tme s shown n Fgure 8. It s easer for a small number of nodes to be synchronzed wthn a short perod or tme. When the number of nodes ncreases to, an equal phase offset s formed, and the nodes are synchronzed as a result of the nteracton between the nodes, although the tme untl the synchronzed state s reached s longer as compared to the case of 4 nodes. However, 2 nodes cannot be synchronzed due to the nsuffcent control of average error, and as a result, the average error keeps fluctuatng and the oscllaton cannot converge to a stable state. The reason for ths falure can be descrbed as follows. In ths smulaton, the node transmts 4 bts of data to the snk wth a transmsson speed of 5 kbps every 6 ms. The transmsson of one data packet requres 4 [bts] / 5 [kbps] = 8 [ms]. Snce the transmsson wdth s 6 ms and the tme slot s 8 ms, perfect ant-phase synchronzaton provdes alternate transmsson for up to 2 nodes. However, such a stuaton s dffcult to realze n practce, and transmsson falures nevtably occur n the process of synchronzaton (Fgure 8(b)). The transmsson falure nterrupts the node from broadcastng the frng nformaton, and consequently phase control s not performed properly and the average error ncreases. The teraton of ths operaton leads to the falure of ant-phase synchronzaton n the case of 2 nodes. Thus, the number of transmsson nodes whch can be synchronzed by ant-phase synchronzaton s constraned by the access perod. Transmsson Falure Probablty Fg nodes nodes 2 nodes (a) Transton of average error. 4 nodes nodes 2 nodes (b) Transton of transmsson falure probablty. Influence of number of nodes on ant-phase synchronzaton. C. Robustness aganst Perturbatons The reason for adoptng a bologcal system n ths method s ts robustness aganst perturbatons. In wreless communcaton n sensor networks, rado waves are shadowed by obstacles and fade as a result of the nterference of rado waves. The energy of the nodes can thus be depleted and the node mght cease to functon n the case of such an unexpected falure. Furthermore, a node can be added to the network n order to replace a faled node. In ths secton, we regard the packet loss and the changes n topology nduced by the addton and the falure of nodes as perturbatons, and show that the self-organzed ant-phase synchronzaton method s robust aganst such perturbatons. The nfluence that the packet loss brngs to average error and transmsson falure s shown n Fgure 9. In ths smulaton, a packet s dropped randomly based on packet loss rate and does

6 Number of Transmsson Falure Fg. 9. Packet Loss Rate Influence of a packet loss Number of Transmsson Falure Relatve Frng Tme (a) Transton of relatve phase offset. Relatve Phase Offset Average error Transmsson Falure Probablty Transmsson Falure Probablty (a) Transson of relatve phase offset. (b) Transton of average error and transmsson falure probablty Transmsson Falure Probablty (b) Transson of average error and transmsson falure probablty. Fg.. Performance of the network under the stuaton where a packet loss rate s 2. Transmsson Falure Probablty Fg.. Influence caused by the change of topology: Addton and falure of the node. not reach to the destnaton. In the envronment where packet loss hardly happens, node adjusts the phase wth sutable nterval to other nodes and a precse ant-phase synchronzaton s performed. Although several tmes of transmsson falure appear, t shall be allowed snce the node has random phase n the ntal condton. Even the synchronous accuracy falls as the packet loss rate ncreases, the phase offset among nodes n the envronment of packet loss rate 2 s mantaned at an acceptable level and data transmsson s carred out wthout falure. Fgure shows the result n ths condton. The phase moves wth fluctuaton due to the falure of phase control caused by the packet loss (Fgure (a)). Eventually, node shfts the phase and keeps the synchronzed state wth recevng the nfluence of packet loss. In the envronment where the packet loss happens frequently (packet loss rate = ), as the node cannot acheve enough nteractons between neghborng nodes for stable ant-phase synchronzaton, the

7 overlap of phase leads the transmsson falure. Yet t s not perfect n the envronment where the packet loss occurs very often, the proposal shows robustness aganst packet loss. The unform dependence on the nformaton brngs robustness of self-organzng method aganst a packet loss. For nstance, the nfluence of packet loss becomes large n centralzed control snce the node located on the lower layer of herarchy decdes ts operaton dependng on the nformaton from the node of the hgher layer. Several methods are known as a soluton of packet loss such as ACK (ACKnowledgement) where a recevng node reples a recepton confrmaton to a transmttng node, and FEC (Forward Error Collecton) whch carres out an error collecton, there are also demerts on those methods such as an ncrease of control packet and an extenson of delay. Not herarchcal but the local exchange of nformaton on self-organzng control yelds robustness aganst packet loss wthout executng those measures. Subsequently, we confrm that the proposed method restores the ant-phase synchronzed state by performng phase control after the addton or the falure of a node. Three nodes wth random phases are added to the network at 2 seconds, and three nodes fal at 5 seconds from ntaton. Fgure shows that nodes wth random phases n the ntal state mmedately converge to a stable ant-phase synchronzaton state. At 2 seconds, the average error decreases and the synchronzed state s destroyed due to the addton of nodes. As the transmsson has been almost smultaneous up untl that tme, transmsson falure arses as carrer sensng s performed over the maxmum back-off tme on CSMA/CA (Fgure (b)). However, the node adjusts the phase n a selforganzng manner aganst the addton of nodes, and the antphase synchronzaton state s restored wthn a short perod of tme. The same performance can be confrmed n the case of falure of nodes. Self-organzed control s characterzed by such robustness aganst changes n topology due to ts ntrnsc functon of local nteractons. In centralzed control, f the node whch plays an mportant role (such as a cluster head) fals, ordnary nodes stop functonng properly wthout recevng orders from that central node. On the other hand, a task s equally dstrbuted to nodes n self-organzed control, and the system s not nfluenced by the rsks assocated wth centralzed control. D. Comparson wth other schemes In order to understand the features of the proposed method, we perform a comparatve evaluaton wth three other schemes. DESYNC [] s a dstrbuted ant-phase synchronzaton scheme whch acheves a synchronzed state by adjustng the phase on the bass of nformaton from two coupled nodes. Random gves random transmsson tmng to the nodes, whle Ideal TDMA uses an deal value whch provdes optmal schedulng. The MAC layer of the frst two methods (DESYNC and Random) s based on CSMA/CA, and the same topology s used n the smulaton. Fgure 2 shows the nfluence of the traffc, namely the number of data generated by a node, on each scheme. The proposed method acheves a hgh Data Collecton Rato Proposal DESYNC Random Ideal TDMA Messages per Second Fg. 2. Comparson of data collecton rato. data collecton rato n the case of low traffc by reducng the number of data transmsson falures. As the traffc ncreases, the data collecton rato decreases due to falures of data transmsson caused by too much traffc over the wdth of the access perod. Although the proposed method does not reach an deal value n such excessve traffc, t mantans a hgher data collecton rato than the random control method. The dfference s manly due to the choce of couplng coeffcent. The advantage of the proposed method s the feasblty of extenson to mult-hop networks snce the stmulus n the proposed method arrves from all nodes, whle n DESYNC t arrves from only two nodes. The comparson between selforganzng and dstrbuted control s a crucal pont n terms of synchronous stablty, extendblty, robustness, and so forth, whch wll be examned n future work. V. CONCLUSION AND POSSIBLE EXTENSIONS Robustness, adaptablty and scalablty are essental features for managng complex and dverse networks. In ths paper, we ntroduced a self-organzng schedulng scheme nspred by frog callng behavor as a method for fulfllng such requrements. We performed evaluatons through computer smulatons n a sngle-hop network for a phase control method nspred by the alternate callng behavor of Japanese tree frogs. The smulaton results showed that phase control reduces the transmsson falures by applyng antphase synchronzaton, regardless of the number of nodes. In addton, robustness aganst packet loss and changes n topology was confrmed, and stable ant-phase synchronzaton was mantaned by realzng adaptve response to perturbatons. Research on ant-phase synchronzaton s a relatvely new feld, and several factors are yet to be explored. In order to prove the feasblty of the convergence to a stable ant-phase synchronzed state, t s necessary to perform mathematcal analyss of the synchronous stablty of the phase shft functon. The phase control mechansm should be mproved n order to acheve extendblty to mult-hop networks, whch

8 also consders the hdden termnal problem. The comparatve evaluaton of the proposed method wth dstrbuted methods from the vewpont of the transmsson of nformaton would reflect the benefts of both methods. ACKNOWLEDGEMENT Ths research was supported n part by the Global COE (Centers of Excellence) Program of the Mnstry of Educaton, Culture, Sports, Scence and Technology, Japan. REFERENCES [] H. Ktano, Bologcal robustness, Nature Revews Genetcs, vol. 5, pp , Nov. 24. [2] F. Dressler, Self-organzaton n sensor and actor networks. Wley, Jan. 27. [3] Y. Zhang, L. Kuhn, and M. Fromherz, Improvements on ant routng for sensor networks, n Proceedngs of the Fourth Internatonal Workshop on Ant Colony Optmzaton and Swarm Intellgence, pp , July 24. [4] H. Chan and A. Perrg, ACE: an emergent algorthm for hghly unform cluster formaton, n Proceedngs of the Frst European Workshop on Wreless Sensor Networks (EWSN 24), pp. 54 7, Jan. 24. [5] R. E. Mrollo and S. H. Strogatz, Synchronzaton of pulse-coupled bologcal oscllators, Journal on Appled Mathematcs, vol. 5, pp , Dec. 99. [6] A. Mutazono, M. Sugano, and M. Murata, Evaluaton of robustness n tme synchronzaton for sensor networks, n Proceedngs of the 2nd Internatonal Conferenece on Bo-Inspred Models of Network, Informaton, and Computng Systems (BIONETICS 27), pp , Dec. 27. [7] L.-Y. Cao and Y.-C. La, Antphase synchronsm n chaotc systems, Physcal Revew E, vol. 58, pp , July 998. [8] I. Ahara, S. Hora, H. Ktahata, K. Ahara, and K. Yoshkawa, Dynamcal callng behavors expermentally observed n Japanese tree frogs (Hyla japonca), IEICE Trans Fundamentals, vol. E9-A, pp , 27. [9] W.E.Duellman and L.Trueb,Bology of amphbans. Johns Hopkns Unversty Press, Mar [] H. C. Gerhardt and F. Huber, Acoustc communcaton n nsects and anurans: common problems and dverse solutons. Unversty of Chcago Press, July 22. [] J. Degesys, I. Rose, A. Patel, and R. Nagpal, DESYNC: Self-organzng desynchronzaton and TDMA on wreless sensor networks, n Proceedngs of the 6th Internatonal Conference on Informaton Processng n Sensor Networks (IPSN 27), pp. 2, Apr. 27. [2] J. Degesys and R. Nagpal, Towards desynchronzaton of mult-hop topologes, n Proceedngs of the Second IEEE Internatonal Conference on Self-Adaptve and Self-Organzng Systems (SASO 28), pp , Oct. 28. [3] M. B. H. Rhouma and H. Frgu, Self-organzaton of pulse-coupled oscllators wth applcaton to clusterng, IEEE Transactons on Pattern Analyss and Machne Intellgence, vol. 23, pp. 8 95, Feb. 2. [4] Q. Cao, T. Abdelzaher, T. He, and J. Stankovc, Towards optmal sleep schedulng n sensor networks for rare-event detecton, n Proceedngs of the 4th Internatonal Symposum on Informaton Processng n Sensor Networks (IPSN 25), Apr. 25. [5] K. Sekyama, Y. Kubo, S. Fukunaga, and M. Date, Phase dffuson tme dvson method for wreless communcaton network, n Industral Electroncs Socety, 24. IECON 24. 3th Annual Conference of IEEE, vol. 3, Nov. 24. [6] I. Ahara, H. Ktahata, K. Yoshkawa, and K. Ahara, Mathematcal modelng of frogs callng behavor and ts possble applcaton to artfcal lfe and robotcs, Artfcal Lfe and Robotcs, vol. 2, pp , Mar. 28.