Traveling Waves Solutions for Delayed Temporally Discrete Non-Local Reaction-Diffusion Equation

This paper deals with the existence of traveling wave solutions to a delayed temporally discrete non-local reaction diffusion equation model, which has been derived recently for a single species with age structure. When the birth function satisfies monotonic condition, we obtained the traveling wavefront by using upper and lower solution methods together with monotonic iteration techniques. Otherwise, without the monotonicity assumption for birth function, we constructed two auxiliary equations. By means of the traveling wavefronts of the auxiliary equations, using the Schauder’ fixed point theorem, we proved the existence of a traveling wave solution to the equation under consideration with speed c>c*, where c*>0 is some constant. We found that the delayed temporally discrete non-local reaction diffusion equation possesses the dynamical consistency with its time continuous counterpart at least in the sense of the existence of traveling wave solutions.

MENGOMUNIKASIKAN KETELADANAN PANJI

The current proposed discussion is related to the complexity that is analyzed based on the stage of thinking.This happens because the current turn of the era which 'back and forth' turns out into a cultural cross. Not monitoredin detail, followed by a changing educational system, and not necessarily in tune with the needs and expectations ofgenerations of "X" and "Y" in the present. In this connection, the idea of harmony can be learned from variousfolklore, which is common in speech stories or by using role models with the following characteristics; 1) always presentas the savior of the kingdom, 2) a consistent figure in the family (in the world of love and the protection of hisgeneration), 3) the original figure of the archipelago earth, not imported figures. All three of these are in the story / play-story of Folk Art Performing/Panji Tradition. Apresiator Mapping in the Digital Age Culture today and thefuture will be more complex, because it can not be separated from non-cultural factors, such as industry, economics,politics and technology. Therefore, the birth function of Review on Transfer Modes based on consideration is to observethe development of digital technology and information technology, increasingly supporting the transformation (Budiman,2012: ii). Considering ethnic and sub ethnic cultures, the digital age, the transfer of modes and regulations of"Cultural Progress", communicating the Panji Oral Tradition can be carried out as follows; 1) Direct or face-to-facecommunication, by way of storytelling, staging folk/traditional performances, effective in 3 T areas (disadvantaged,leading, marginalized) 2) Media communication, 3) Communication in modern areas/no communication systembarriers.

Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function

A single species population model is investigated, where the discrete maturation delay and the Ricker birth function are incorporated. The threshold determining the global stability of the trivial equilibrium and the existence of the positive equilibrium is obtained. The necessary and sufficient conditions ensuring the local asymptotical stability of the positive equilibrium are given by applying the Pontryagin's method. The effect of all the parameter values on the local stability of the positive equilibrium is analyzed. The obtained results show the existence of stability switch and provide a method of computing maturation times at which the stability switch occurs. Numerical simulations illustrate that chaos may occur for the model, and the associated parameter bifurcation diagrams are given for certain values of the parameters.

HOPF BIFURCATION IN AN AGE-DEPENDENT POPULATION MODEL WITH DELAYED BIRTH PROCESS

This paper is devoted to the study of an age-dependent population system with Riker type birth function. The time lag factor is considered for the birth process. We investigate some dynamical properties of the equation by using C0-semigroup theory, through which we obtain some conditions of asymptotical stability and Hopf bifurcation occurring at positive steady state for the system.

Uniqueness of fast travelling fronts in reaction–diffusion equations with delay

We consider positive travelling fronts, u ( t , x )= ϕ ( ν . x + ct ), ϕ (−∞)=0, ϕ (∞)= κ , of the equation u t ( t , x )=Δ u ( t , x )− u ( t , x )+ g ( u ( t − h , x )), x ∈ m . This equation is assumed to have exactly two non-negative equilibria: u 1 ≡0 and u 2 ≡ κ >0, but the birth function g ∈ C 2 ( , ) may be non-monotone on [0, κ ]. We are therefore interested in the so-called monostable case of the time-delayed reaction–diffusion equation. Our main result shows that for every fixed and sufficiently large velocity c , the positive travelling front ϕ ( ν . x + ct ) is unique (modulo translations). Note that ϕ may be non-monotone. To prove uniqueness, we introduce a small parameter ϵ =1/ c and realize a Lyapunov–Schmidt reduction in a scale of Banach spaces.