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We study a nonhierarchical tritrophic system, whose predator-prey interactions are described by the rock-paper-scissors game rules. In our stochastic simulations, individuals may move strategically towards the direction with more conspecifics to form clumps instead of moving aimlessly on the lattice. Considering that the conditioning to move gregariously depends on the organism's physical and cognitive abilities, we introduce a maximum distance an individual can perceive the environment and a minimum conditioning level to perform the gregarious movement. We investigate the pattern formation and compute the average size of the single-species spatial domains emerging from the grouping behaviour. The results reveal that the defence tactic reduces the predation risk significantly, being more profitable if individuals perceive further distances, thus creating bigger groups. Our outcomes show that the species with more conditioned organisms dominate the cyclic spatial game, controlling most of the territory. On the other hand, the species with fewer individuals ready to perform aggregation strategy gives its predator the chance to fill the more significant fraction of the grid. The spatial interactions assumed in our numerical experiments constitute a data set that may help biologists and data scientists understand how local interactions influence ecosystem dynamics., Comment: 8 pages, 10 figures

We study a three-species cyclic game system where organisms face a contagious disease whose virulence may change by a pathogen mutation. As a responsive defence strategy, organisms' mobility is restricted to reduce disease dissemination in the system. The impact of the collective self-preservation strategy on the disease infection risk is investigated by performing stochastic simulations of the spatial version of the rock-paper-scissors game. Our outcomes show that the mobility control strategy induces plasticity in the spatial patterns with groups of organisms of the same species inhabiting spatial domains whose characteristic length scales depend on the level of dispersal restrictions. The spatial organisation plasticity allows the ecosystems to adapt to minimise the individuals' disease contamination risk if an eventual pathogen alters the disease virulence. We discover that if a pathogen mutation makes the disease more transmissible or less lethal, the organisms benefit more if the mobility is not strongly restricted, thus forming large spatial domains. Conversely, the benefits of protecting against a pathogen causing a less contagious or deadlier disease are maximised if the average size of groups of individuals of the same species is significantly limited, reducing the dimensions of groups of organisms significantly. Our findings may help biologists understand the effects of dispersal control as a conservation strategy in ecosystems affected by epidemic outbreaks., Comment: 8 pages, 8 figures

This Special Issue comprises the first collection of papers submitted by the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA), as well as outstanding scholars working in the core research fields of MCA [...]

This white paper discusses the evolution of the satellite radio industry during its first decade. Since their inception, both Sirius & XM have gone through major developments as well as changes include the acquisition of Sirius by XM in March 2008. This paper is an important to the current literature in this field as it preserves the history of the origins and development of the satellite radio industry during its first and most important decade.

The measurements by lab-on-a-chip devices are very interesting regarding the reduction of reagents, time and cost. In this paper, we have described the construction and application of a new device based on colorimetric measurements using a smartphone camera and a microfluidic paper-based device (μPAD), both fixed in supports obtained through 3D printing, employing a polylactic acid filament. The μPAD was evaluated as a water quality index device by colorimetric monitoring of water hardness (Ca2+ and Mg2+), total phenols (catechol), and pH. Under optimized parameters, the proposed method presented a linear range between 20 and 560 mg L−1 for Ca2+ and Mg2+(hardness), 0.20 to 16 mg L−1 of catechol and pH from 4.7 to 12, and limits of detection of 0.083 mg L−1, 0.124 mg L−1 and 0.262, for water hardness, catechol, and pH, respectively. The proposed device was successfully applied for the quality monitoring of the distribution of water samples.

Modeling morphological and hydraulic properties of thin porous media, such as filter layers and papers is highly relevant to various industries. In our previous studies, the X-ray tomography and FIB-SEM methods were applied to capture micro- and nano-scale pores in uncoated paper and coated layer, respectively. Here, the reconstructed pore structures were used to investigate two-phase water imbibition in these porous media. The obtained pore size distributions showed a log-normal probability density function. Such a distribution, together with concepts from critical path analysis and percolation theory, was applied to calculate relative permeability over a wide range of water saturations. Comparison with pore-scale numerical simulations showed the capability of this method to estimate water relative permeability for coated and uncoated papers.

The objective of this study was to characterize the properties of pulp and paper manufactured from two agricultural residues namely, wheat straw (Triticum aestivum L. em Thell.) and date palm midribs (Phoenix dactylifera L.) widely available in Saudi Arabia by employing soda-anthraquinone (AQ) pulping process. Specimens from cedar wood (Juniperus procera Hochst. ex Endl.) wood was also used as control samples. Chemical and the morphological characteristics of all three types of raw materials in addition to basic properties of hand sheets made from such resources were evaluated. The results indicated that wheat straw had the highest hemicellulose and ash values of 35% and 7% and the lowest lignin content value of 18%, respectively. The fibre length of the both palm fronds and wheat straw was lower than that of 2.2 mm which was found for J. procera. Overall strength properties of the handsheet made from two agricultural raw materials were significantly lower than those made from J. procera pulp. Wheat straw handsheets also had higher strength properties than those made from date palm midribs with an exception of their tear index. Based on the results of this study it appears that both types of raw materials, date palm midribs and wheat straw could have a potential to manufacture pulp and paper with accepted properties so that such underutilized species can be converted into value-added products.

We examine the role of count conservation when derived network matrices are obtained from linked network matrices using an outer product decomposition. It is seen that a full counting operation conserves the count of pathways between nodal variables while a fractional counting operation conserves the count of the nodal variable. We use the cases of co-referencing (bibliographic coupling) and co-citation with a simple citation network to illustrate the ideas.

This work is a contribution to the Project UIDB/04035/2020, funded by FCT - Fundacao para a Ciencia e a Tecnologia, Portugal.

Paper is a complex material consisting of a network of cellulose fibres at the micro-level. During manufacturing, the network is dried under restraint conditions due to tension in the paper web in machine direction. This gives rise to internal strains that are stored in the produced sheet. Upon exposure to a moisture cycle, these strains may be released. This results in permanent shrinkage that may cause instabilities such as curl or waviness of the sheet. The prime objective of this paper is to model this irreversible shrinkage and to link its magnitude to the properties of the fibres and of the network. For this purpose, randomly generated fibrous networks of different coverages (i.e. ratio of the area occupied by fibres and that of the sheet) are modeled by means of a periodic representative volume element (RVE). Within such RVEs, a finite element method combined with a kinematic hardening plasticity model at the scale of the fibres is used to capture the irreversible response. The computational results obtained demonstrate that the magnitude of the irreversible strains increases with coverage until a certain coverage and beyond that coverage decreases in magnitude. This phenomenon is explained by considering the area fraction of free-standing fibre segments relative to bonded fibre segments in the network. A structure–property dependency of irreversible strains at the sheet-level on the micro-structural parameters of the network is thereby established., SCOPUS: ar.j, info:eu-repo/semantics/published

This comment is devoted to the paper "Exact solutions of nonlinear diffusion-convection-reaction equation: A Lie symmetry approach" (CNSNS, vol. 67 (2019), 253-263) in which several results are not new because were derived much earlier. Moreover, some results in the paper are incorrect or incomplete., Commun Nonlinear Sci Numer Simulat

In this work, we improve and correct some results in the paper by Proinov (J Fixed Point Theory Appl 22:1–27, 2020).

International audience; We clarify some analytical expressions existing in the literature, • Within the correct formulae we conclude that there is no need for an ad hoc improvement on the opposite to the title paper, • We highlight the symmetry properties of the function to be integrated in order to agree with the usual assumptions made to derive the Kramers-Kronig relations, • The analytical formula we provide may be used to increase the accuracy of the "Poor Man's Kramers-Kronig analysis" method and the "Kramers-Kronig constrained variational analysis" method.

Organisms may respond to local stimuli that benefit or threaten their fitness. The adaptive movement behaviour may allow individuals to adjust their speed to maximise the chances of being in comfort zones, where death risk is minimal. We investigate spatial cyclic models where the rock-paper-scissors game rules describe the nonhierarchical dominance. We assume that organisms of one out of the species can control the mobility rate in response to the information obtained from scanning the environment. Running a series of stochastic simulations, we quantify the effects of the movement strategy on the spatial patterns and population dynamics. Our findings show that the ability to change mobility to adapt to environmental clues is not reflected in an advantage in cyclic spatial games. The adaptive movement provokes a delay in the spatial domains occupied by the species in the spiral waves, making the group more vulnerable to the advance of the dominant species and less efficient in taking territory from the dominated species. Our outcomes also show that the effects of adaptive movement behaviour accentuate whether most individuals have a long-range neighbourhood perception. Our results may be helpful for biologists and data scientists to comprehend the dynamics of ecosystems where adaptive processes are fundamental., Comment: 8 pages, 7 figures

Early paper manufacturing used sieve-like molds through which paper pulp was drained. Two pieces of paper are called moldmates if they were made using the same mold. When a large body of one artist?s work on paper exists, the identification of moldmates can help in establishing chronology, suggest paper preferences, and indicate periods of intense activity of the artist. Rembrandt is an especially good example. With several thousand prints in existence today, the study of Rembrandt?s prints has occupied scholars for over two centuries, and the study of his printing papers occupies a prominent place within this scholarship [1]. This article examines the feasibility of moldmate identification via chain-line pattern matching and conducts a series of experiments that demonstrate how accurately the measurements can be made, how straight and parallel the lines may be, and provides a rule of thumb for the number of chain lines required for accurate moldmate identification using a simplified model. The problem of identifying moldmates among Rembrandt?s prints is presented as a pair of image/signal processing tasks; our strategy is to provide basic solutions to these tasks and to then reveal the shortcomings of these solutions in the hopes of encouraging future work in the signal processing community. With the support of the Morgan Library & Museum and the Metropolitan Museum of Art, both of which are in New York, we have made high-resolution data available [2] to facilitate this quest.

In this study we investigated the underlying mechanisms of coffee stain formation on paper - a porous substrate. When a drop of aqueous liquid containing dispersed materials dries on paper, the faster water evaporation rate at the edge of the drop drives the redistribution of the dispersed materials to the edge of the drop-covered area on paper. Deegan's discovery has been accepted as the "coffee ring" phenomenon, which has wide implications. However, stains left by dried aqueous liquids on paper are not always ring-shaped. This is because, besides Deegan's coffee ring effect, the transport of dispersed materials in porous media is affected by chromatographic and filtration effects, which are highly dependent upon the properties of the substrates. In this work we clarify the influences of different mechanisms to the dispersed materials redistribution in paper. Refereed/Peer-reviewed

Our society is facing serious environmental challenges related to climate change, pollution, diminishing resources, and biodiversity loss. Such problems are often ill-defined and are characterized by high uncertainty. Environmental decisions have strong impacts on society and demand clear and transparent trade-offs across values and priorities of stakeholder groups. This Feature Issue on Environmental Decisions includes papers focused on important environmental applications approached through various disciplinary backgrounds. The papers highlight advanced–often interdisciplinary–methodological approaches and include the perspectives of different stakeholders in the process of environmental decision-making. A wide range of methods are explored, ranging from a comprehensive review (for sustainable transport by Marleau Donais et al.) to an opinion paper proposing the use of Records of Engagement and Decision-making (RoED; by Cockerill et al.). Stakeholder engagement and preference elicitation required the development of new aggregation models for Multi-Criteria Decision Analysis (MCDA; by Reichert et al.). The integration of Cost-Benefit Analysis (CBA) with MCDA was found to be necessary in practice (by Liu et al.; Marleau Donais et al.). MCDA was extended to include the spatial dimension by integrating Geographic Information Systems (GIS; by Guay et al.; Schito et al.). The importance of considering the resilience of systems to better respond to and recover from unpredictable risks was emphasized (by Leyerer et al.; Mustajoki and Marttunen). These papers demonstrate the richness of approaches to environmental decision-making. Environmental issues offer ample exciting research opportunities to a broader scientific community. We encourage the readers of this Feature Issue—and of EJDP—to engage in environmental decision-making projects to support emerging societal needs.

The cross-directional model predictive control (CD-MPC) tuning problem is investigated for multiple-array paper-making process with parametric uncertainty. A systematic spatial tuning method is proposed to tune the penalty matrices such that the harmful high frequency elements in each actuator profile can be eliminated. A multivariable temporal filter is employed to adjust the output references, and a temporal tuning algorithm is developed for the filter parameters to achieve the pre-specified 2 σ performance indices. The computational time of the proposed methods is reduced via event-based sampling strategy. The effectiveness of the techniques is shown via a CD system from paper-making industry.

We present a computational framework for stability analysis of systems of coupled linear Partial-Differential Equations (PDEs). The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichlet, Neuman and mixed boundary conditions. The results in this paper apply to systems with a single spatial variable. We exploit a new concept of state for PDE systems which allows us to include the boundary conditions directly in the dynamics of the PDE. The resulting algorithms are implemented in Matlab, tested on several motivating and illustrative examples, and the codes have been posted online. Numerical testing indicates the approach has little or no conservatism for a large class of systems and can analyze systems of up to 20 coupled PDEs.

In recent years, paper has been used as an alternative to traditional substrate materials in the development of strain sensors and accelerometers due to its flexibility, disposability due to environment low footprint and low cost. A lack of knowledge about the sources of nonlinearity in the mechanical behavior of paper makes difficult to consistently predict its performance. The characterization procedures available in the literature are based on both static and dynamic loading as a first attempt to describe the elastic behavior of paper in sensing applications. However, these procedures do not reveal the necessary information to describe the elastic behavior of paper under dynamic excitation. In this work, the nonlinear dynamic response of a harmonically excited paper-based cantilever beam is studied. A lumped model with a quadratic nonlinearity is adopted to describe the nonlinear response of paper-based cantilever beams. The obtained results show that the nonlinear resonance frequency response is dependent on the intrinsic properties of paper when discarding hygrothermal variations of paper as the main source of nonlinear behavior. It was found that the estimation of two nonlinear elastic parameters, α p (hysteresis nonlinear parameter) and E 0 (linear elastic modulus) could yield an improved description of the elastic behavior of paper subjected to vibrations. It was concluded that the existing paper characterization standards should be adapted to better predict the dynamic behavior of paper-based mechanical systems. Different types of paper materials were analyzed to study the influence of the intrinsic characteristics of paper on the nonlinear parameters.

A number of problems associated with dimensional stability of paper products have to do with hygroexpansion in response to changes in humidity or moisture content. The main underlying mechanism of hygroexpansion in paper is the effect of the change of fiber cross-sections transferred through fiber bonds. In fact, the transverse expansion of fibers can be an order of magnitude greater than the longitudinal expansion. Addressing such problems using modeling on the microscale is associated with large computational costs since both the bonds and the fibers need to be resolved. We present a method for modeling the hygro or thermal expansion of interconnected fiber networks modeled with beam elements and connected through beam-to-beam contact. Being a line structure, beams can only support pointwise contact, which poses a challenge for modeling the force transfer induced by the deformation of the cross-sections at the contact point. The idea of implementing the stress transfer is to use a concurrent multiscale approach in which the bond level is resolved in detail using the configuration of the fibers and the computed strains are passed over to the beam elements. We verify and prove the applicability of this approach by comparing it with continuum models. We demonstrate the advantage of using this approach in terms of its tremendous saving in time. The use of beam models for modeling the hygro- or thermal expansion of fiber networks enables considering relevant sizes in the problems involving dimensional stability, in particular those associated with embedded inhomogeneities. We will show the applicability of the model by providing insights into published experimental observations on the hygroexpansion properties of paper products. Finally, we will demonstrate that the use of a 2D model to simulate the inter-fiber bonds in a network, not only leads to underestimation of out-of-plane deformations, but also to overestimation of the contribution of the transverse deformation of fibers to the in-plane dimensional change of the network.

The papers in this issue provide an excellent example of how pertinent distinctions which emerge from analysis of significant data sets can be communicated to colleagues and used to make sense of observations. The distinctions are vividly described, illustrated and exemplified, and used to chart maturation in student use of examples from middle school, through high school and into university. Curiously, no corresponding maturation was detected in students’ choice of examples to use for themselves. Contrast was detected between the way students used the same examples for comprehending a conjecture and testing its validity, and the way that some mathematicians used specifically constructed examples for locating underlying structure. What emerged for me from reading these papers is confirmation of the central role of attention, the productiveness of engaging students at the earliest ages and throughout their schooling with the detection and expression of generality, and the importance of being explicit about the scope of generality encompassed by a claim. Purposeful use of examples by students could be expected to develop as teachers explicitly use examples purposefully with and for students. A reasonable conjecture might be that getting students to be explicit about the scope of generality, of possible variation of which they are aware, might shed light on obstacles and barriers to reasoning which might otherwise lead to proof.

The effect of nano-wollastonite and Aspergillus niger fungus on permeability of historical and common paper was studied here. Specimens were immersed in aqueous wollastonite nano-suspension (NW) at 10, 20, 30, and 40% concentration, and their permeability was finally compared with that obtained from control specimens. Permeability of each specimen was measured before and after the immersion in NW. To fix solid particles on NW-treated specimens, polyvinyl acetate (PVA) was mixed in all treatments. Results showed that wollastonite significantly limited the growth of A. niger. Permeability of historical specimens was significantly lower than that of the common paper, 29 in comparison to 190 cm3.s−1, respectively. This was due to the higher density in the historical paper, providing lower empty voids and spaces for fluid to pass through. Fungi culture resulted in significant decrease in both paper types. In fact, fungal hyphae penetrated into the specimens, eventually blocking the paths through which fluid could transfer. High significant R-square values were found between permeability values before and after the exposure to A. niger. It was concluded that permeability is closely correlated to the density of paper, and it has a significant effect on the potentiality of fungi hyphae to be penetrated into the texture of papers, affecting the weight loss values. Moreover, NW-suspension can be used to decrease permeability as well as susceptibility to fungal attack.

Communicability functions quantify the flow of information between two nodes of a network. In this work, we use them to explore the concept of the influence of a paper in a citation network. These functions depend on a parameter. By varying the parameter in a continuous way we explore different definitions of influence. We study six citation networks, three from physics and three from computer science. As a benchmark, we compare our results against two frequently used measures: the number of citations of a paper and the PageRank algorithm. We show that the ranking of the articles in a network can be varied from being equivalent to the ranking obtained from the number of citations to a behaviour tending to the eigenvector centrality, these limits correspond to small and large values of the communicability-function parameter, respectively. At an intermediate value of the parameter a PageRank-like behaviour is recovered. As a test case, we apply communicability functions to two sets of articles, where at least one author of each paper was awarded a Nobel Prize for the research presented in the corresponding article.

In this note we offer some criticism on the paper “On an identity for zeros of Bessel functions” by Baricz et al. [3] . The paper gives identities of type Stieltjes–Calogero for the sums of reciprocals of differences of fourth powers of zeros of Bessel functions. Although interesting in principle, by containing one too many sums of similar complexity the identities fail to convey the true spirit of the work of Stieltjes and Calogero. We rectify this by providing what we think is the correct type of identity for the above-said sums, in the general setup of entire functions of order

Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species.

The papers in this special issue were presented at the 2018 17th International Workshop on Data Mining in Bioinformatics (BIOKDD), held in conjunction with the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. The Workshop was held on August 20, 2018 in London, UK.

Giving the proper citations, it is shown that, except of Lemma 2.4 and Theorem 2.6, almost all the results of the paper in the title have been previously published for ordered hypersemigroups in Eur. J. Pure Appl. Math. and they are not new. There are also two results obtained from ordered semigroups just putting a ``$\circ$" instead of ``$\cdot$" (that isn't a correct way to work), without reference to ordered semigroups on which the results on ordered hypersemigroups are based. One of them can be obtained as corollary to a theorem in Eur. J. Pure Appl. Math. as well, and it is not new.

Inter-turn insulation plays a major role in the dielectric integrity of any transformer. Though the inter-turn insulation thickness is designed based on standard lightning impulse (LI) voltage distribution, the insulation fails due to various types of overvoltages from switching impulse (SI) to very fast transient overvoltages (VFTO). Moreover, the insulation gets degraded due to many factors such as service ageing, exposure to repeated applications of overvoltages due to various reasons, etc. The effect of the repeated impulses is characterized using the voltage–number (V–N) characteristics recommended by CIGRE Working group C4.302. Based on the design and rating of the transformer, the thickness of the inter-turn insulation is normally changed. To quantify and compare the impulse breakdown strength and degradation due to repeated impulses under SI, LI and VFTO, different thicknesses of oil impregnated paper, ranging from 0.25 to 0.75 mm are considered. Experiments are carried out to obtain the V–N characteristics for all the cases. V–N characteristics are mathematically modeled by enhancing the existing exponential model to incorporate the thickness of insulation and are then validated experimentally. Based on the model parameters, the effect of the various waveshapes and the degradation due to repeated impulses are quantified and compared with the standard LI.

Peta Wisata Bahari (PWB) dibuat untuk menyajikan informasi tentang lokasi tempat – tempat wisata, ada banyak ikon/simbol yang mudah dikenali dan disertai informasi singkat tentang tempat tersebut, serta sebagai sarana pendukung bantu bernavigasi dalam pelayaran sehingga mempermudah para wisatawan dalam menentukan pilihan wisata-wisata yang ada yang akan dijadikan sebagai destinasi wisata. PWB Wilayah Labuan Bajo dan Pulau Komodo yang telah sesuai dapat digunakan oleh para pengguna dan kapal-kapal wisatawan secara efektif.Pembuatan PWB di Pushidrosal saat ini menggunakan perangkat lunak CARIS GIS 4.5 dengan proses tahapan yang panjang dan waktu yang cukup lama. Caris Paper Chart Composer 2.1 (CARIS PCC 2.1) merupakan perangkat lunak yang mempunyai fungsi sama dengan CARIS GIS 4.5 dalam hal pembuatan peta laut. Tujuan yang ingin dicapai dari penelitian ini adalah tersedianya PWB Wilayah Labuan Bajo dan Pulau Komodo yang sesuai dengan juknis pembuatan PWB dengan proses tahapan pembuatan yang efektif dan efisien. Metode yang digunakan adalah dengan mendigitasi PWB Wilayah Labuan Bajo dan Pulau Komodo berupa raster menggunakan perangkat lunak CARIS PCC 2.1. Hasil digitasi tersebut dikoreksi dengan optimalisasi, validasi dan analisis hingga nilai kesalahan tidak ada yang muncul.

In this work, some counterexamples are given to refute some results reported in the paper by Guo and Li [8] (J Optim Theory Appl 162,(2014), 821-844). We correct the faulty in some of their theorems and we present alternative proofs. Moreover, we extend the definition of approximately pseudo-dissipative in the setting of metrizable topological vector spaces.

The aim of the study was to validate the Portuguese language version of the 10-item Cervantes Scale (CS-10), a self-reporting instrument that assesses menopausal symptoms, and to compare the results (both symptom severity and multigroup invariance) of middle-aged women who completed the questionnaire in paper-and-pencil format (PPF) or in the online format (OF).A total of 292 women, aged 45 to 65 years, completed the questionnaires (PPF = 66; OF = 226). Construct (factorial and convergent) and external validity, as well as reliability and psychometric sensitivity were studied. Multigroup confirmatory factor analysis was performed to compare PPF with OF, regarding the measure's invariance.The CS-10 showed good psychometric properties (ie, factor and external validity), as well as good sensitivity and reliability. The association with the Utian Quality of Life Scale (UQoLS) was significant and positive, though weak. The measured structure was invariant when comparing both subsamples (PPF and OF), evidencing an equivalent structure in both. No differences in reported symptoms were observed between the two subgroups.The Portuguese language version of the CS-10 rendered data with good psychometric properties in a sample of middle-aged Portuguese women. Therefore, it can be used in both clinical and community settings. The weak association between both instruments (UQoLS and CS-10) might be due to the different conceptualization of the quality of life construct: the CS-10 focuses on symptom severity, whereas the UQoLS assesses domains such as work-related or health-related behaviors.

Migration paths of animals are rarely the same. The paths may change according to seasonal and circadian rhythms. We study the effect of temporal migration on population dynamics of rock-paper-scissors (RPS) games with mutation by using the metapopulation dynamic model with two patches. Via mutation, an individual R changes to S with rate μ. All agents move by random walk between two patches and the RPS game is performed in each patch. The migration path between two patches is switched on or off periodically. The dynamics are represented by the reaction-diffusion equations with time-dependent diffusion coefficients in diffusively coupled reactors. We obtain the solutions of time-dependent reaction-diffusion equations numerically and analytically. The time-varying migration path induces complex behavior for the RPS dynamics, depending on the frequency of the periodical path. We find that the phase transitions occur by varying mutation rate μ. The phase transition depends highly on the frequency.