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Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.

Research & information: general --- Mathematics & science --- cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal

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This book is a collection of a series of articles on several aspects of coastal fish biology and ecology. Coastal fish are key components of marine ecosystems, and the aim of this book is to present relevant research on these wonderful animals and to provide insights for future research in this field.

Alexandria pompano --- Slender sunfish --- Kitefin shark --- Crested oarfish --- Barracudina --- eastern Mediterranean Sea --- eastern Sicily --- Batoidea --- elasmobranchs --- diet --- coastal fishery --- fish assemblage --- lower reaches --- Nakdong River --- estuary weir --- marine juveniles --- Trachipteridae --- Ponza Island --- upwelling --- plankton diversity --- Batesian mimicry --- fish eggs --- environmental factors --- spatial factors --- generalized additive model --- remote sensing --- commercial fish species --- Mediterranean Sea --- environmental health --- heavy metals --- biomarkers --- benthic fish --- molecular tools --- cytochrome b --- ribosomal protein gene S7 --- Gobius cruentatus --- Gobius geniporus --- genetic structure --- quantitative fatty acid signature analysis --- aquatic food webs --- dietary estimation --- BRUV --- Ross Sea --- video sampling --- Antarctica --- coastal ecosystem --- video monitoring --- Tropical Eastern Pacific fish assemblage --- Galapagos --- water quality --- anthropogenic pressure --- European hake --- Merluccius merluccius --- fecundity --- somatic indices --- Adriatic Sea --- L50 --- invasive species --- non-indigenous species --- biological control --- prey–predator interactions --- n/a --- prey-predator interactions

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Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.

Research & information: general --- Mathematics & science --- cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal --- cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal

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Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all over the world, studying such problems is inevitable. In this sense, the first step in understanding such problems is the mathematical forms. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done involving fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world. Various methods have been presented and developed to solve such models numerically and analytically. Extracted results are generally in the form of numerical solutions, analytical solutions, approximate solutions and periodic properties. With the help of newly developed computational systems, experts have investigated and modeled such problems. Moreover, their graphical simulations have also been presented in the literature. Their graphical simulations, such as 2D, 3D and contour figures, have also been investigated to obtain more and deeper properties of the real world problem.

fractional kinetic equation --- Riemann–Liouville fractional integral operator --- incomplete I-functions --- Laplace transform --- fractional differential equations --- fractional generalized biologic population --- Sumudu transform --- Adomian decomposition method --- Caputo fractional derivative --- operator theory --- time scales --- integral inequalities --- Burgers’ equation --- reproducing kernel method --- error estimate --- Dirichlet and Neumann boundary conditions --- Caputo derivative --- Laplace transforms --- constant proportional Caputo derivative --- modeling --- Volterra-type fractional integro-differential equation --- Hilfer fractional derivative --- Lorenzo-Hartely function --- generalized Lauricella confluent hypergeometric function --- Elazki transform --- caputo fractional derivative --- predator–prey model --- harvesting rate --- stability analysis --- equilibrium point --- implicit discretization numerical scheme --- the (m + 1/G′)-expansion method --- the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation --- periodic and singular complex wave solutions --- traveling waves solutions --- chaotic finance --- fractional calculus --- Atangana-Baleanu derivative --- uniqueness of the solution --- fixed point theory --- shifted Legendre polynomials --- variable coefficient --- three-point boundary value problem --- modified alpha equation --- Bernoulli sub-equation function method --- rational function solution --- complex solution --- contour surface --- variable exponent --- fractional integral --- maximal operator --- n/a --- Riemann-Liouville fractional integral operator --- Burgers' equation --- predator-prey model --- the (m + 1/G')-expansion method --- the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation

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This book is a collection of a series of articles on several aspects of coastal fish biology and ecology. Coastal fish are key components of marine ecosystems, and the aim of this book is to present relevant research on these wonderful animals and to provide insights for future research in this field.

Research & information: general --- Biology, life sciences --- Zoology & animal sciences --- Alexandria pompano --- Slender sunfish --- Kitefin shark --- Crested oarfish --- Barracudina --- eastern Mediterranean Sea --- eastern Sicily --- Batoidea --- elasmobranchs --- diet --- coastal fishery --- fish assemblage --- lower reaches --- Nakdong River --- estuary weir --- marine juveniles --- Trachipteridae --- Ponza Island --- upwelling --- plankton diversity --- Batesian mimicry --- fish eggs --- environmental factors --- spatial factors --- generalized additive model --- remote sensing --- commercial fish species --- Mediterranean Sea --- environmental health --- heavy metals --- biomarkers --- benthic fish --- molecular tools --- cytochrome b --- ribosomal protein gene S7 --- Gobius cruentatus --- Gobius geniporus --- genetic structure --- quantitative fatty acid signature analysis --- aquatic food webs --- dietary estimation --- BRUV --- Ross Sea --- video sampling --- Antarctica --- coastal ecosystem --- video monitoring --- Tropical Eastern Pacific fish assemblage --- Galapagos --- water quality --- anthropogenic pressure --- European hake --- Merluccius merluccius --- fecundity --- somatic indices --- Adriatic Sea --- L50 --- invasive species --- non-indigenous species --- biological control --- prey-predator interactions --- Alexandria pompano --- Slender sunfish --- Kitefin shark --- Crested oarfish --- Barracudina --- eastern Mediterranean Sea --- eastern Sicily --- Batoidea --- elasmobranchs --- diet --- coastal fishery --- fish assemblage --- lower reaches --- Nakdong River --- estuary weir --- marine juveniles --- Trachipteridae --- Ponza Island --- upwelling --- plankton diversity --- Batesian mimicry --- fish eggs --- environmental factors --- spatial factors --- generalized additive model --- remote sensing --- commercial fish species --- Mediterranean Sea --- environmental health --- heavy metals --- biomarkers --- benthic fish --- molecular tools --- cytochrome b --- ribosomal protein gene S7 --- Gobius cruentatus --- Gobius geniporus --- genetic structure --- quantitative fatty acid signature analysis --- aquatic food webs --- dietary estimation --- BRUV --- Ross Sea --- video sampling --- Antarctica --- coastal ecosystem --- video monitoring --- Tropical Eastern Pacific fish assemblage --- Galapagos --- water quality --- anthropogenic pressure --- European hake --- Merluccius merluccius --- fecundity --- somatic indices --- Adriatic Sea --- L50 --- invasive species --- non-indigenous species --- biological control --- prey-predator interactions