a characterization of decentralized fixed modes in terms of transmission zeros a simple development is given to show that a linear time invariant plant has a decentralized fixed mode at if and only if is a transmission zero of certain subsystems of the plant

curved fronts in the belousov zhabotinskii reaction diffusion systems in r 2 in this paper we consider a diffusion system with the belousov zhabotinskii bz for short chemical reaction following brazhnik and tyson 4 and perez munuzuri et al 45 who predicted v shaped fronts theoretically and discovered v shaped fronts by experiments respectively we give a rigorous mathematical proof of their results we establish the existence of v shaped traveling fronts in r 2 by constructing a proper supersolution and a subsolution furthermore we establish the stability of the v shaped front in r 2 c 2018 elsevier inc all rights reserved

travelling fronts and entire solutions of the fisher kpp equation in ℝn this paper is devoted to time global solutions of the fisher kpp equation in n where f is a c 2 concave function on 0 1 such that f 0 f 1 0 and f 0 on 0 1 it is well known that this equation admits a finite dimensional manifold of planar travelling fronts solutions by considering the mixing of any density of travelling fronts we prove the existence of an infinite dimensional manifold of solutions in particular there are infinite dimensional manifolds of nonplanar travelling fronts and radial solutions furthermore up to an additional assumption a given solution u can be represented in terms of such a mixing of travelling fronts

on fixed modes in decentralized control systems this paper investigates the conditions for existence and the characterization of fixed modes in decentralized multivariable control systems employing local controllers it is shown that for scalar local controllers in the diagonal control structure the necessary and sufficient condition for a system polo at s to be a fixed mode is that s be a transmission zero of all subsystems formed by selecting the same inputs and outputs of the system the results are applied to scalar controllers in any arbitrary control structure and also to non scalar local controllers and similar conditions are obtained examples are discussed for illustration

on the characterization of fixed modes in decentralized control characterizations of decentralized fixed modes in terms of remnant zeros are presented a novel criterion for testing the fixed modes is obtained the result can be used to derive an existing algebraic criterion through a simple rank evaluation of certain matrices

decentralized stabilization and pole assignment for general proper systems considered is the problem of finding existence conditions and a controller synthesis procedure using decentralized control for assigning the poles of a linear time invariant proper system described by a state space model c a b d where no assumption is made regarding the structure of d this problem has direct application to the decentralized stabilization problem decentralized robust servomechanism problem etc and is a nontrivial extension to the standard decentralized problem where it is assumed that the direct feedthrough terms either are absent or have a block diagonal structure

the uniqueness and asymptotic stability of pyramidal traveling fronts in the allen cahn equations abstract this paper studies the uniqueness and the asymptotic stability of a pyramidal traveling front in the three dimensional whole space for a given admissible pyramid we prove that a pyramidal traveling front is uniquely determined and that it is asymptotically stable under the condition that given perturbations decay at infinity for this purpose we characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces moreover we characterize the pyramidal traveling front in another way that is we write it as a combination of two dimensional v form waves on the edges this characterization also uniquely determines a pyramidal traveling front

technical communique a graph theoretic method to find decentralized fixed modes of lti systems this paper deals with the decentralized pole assignability of interconnected systems by means of linear time invariant lti controllers a simple graph theoretic approach is proposed to identify the distinct decentralized fixed modes dfms of the system i e the unrepeated modes which cannot be moved by means of a lti decentralized controller the state space representation of the system is transformed to the decoupled form using a proper change of coordinates for any unrepeated mode a matrix is then computed which resembles the transfer function matrix of the system at some point in the complex plane a bipartite graph is constructed accordingly in terms of the computed matrix now the problem of verifying if this mode is a dfm of the system reduces to checking if the constructed graph has a complete bipartite subgraph with a certain property the sole restriction of this work is that it is only capable of identifying the distinct dfms of a system however it is axiomatic that most of the modes of the real world systems are normally distinct the primary advantage of the present paper is its simplicity compared to the existing ones which often require evaluating the rank of several matrices

convex compact sets in rn 1 give traveling fronts of cooperation diffusion systems in rn abstract this paper studies traveling fronts to cooperation diffusion systems in r n for n 3 we consider n 2 dimensional smooth surfaces as boundaries of strictly convex compact sets in r n 1 and define an equivalence relation between them we prove that there exists a traveling front associated with a given surface and show its stability the associated traveling fronts coincide up to phase transition if and only if the given surfaces satisfy the equivalence relation

a generalized mfd criterion for fixed modes a generalized matrix fraction description mfd criterion for fixed modes with arbitrarily constrained feedback structure is presented the efficiency of the new criterion in structure analysis is illustrated by a numerical example this criterion which generalizes that of b o anderson and d j clements automatica vol 17 p 703 12 1981 is shown to be more convenient in some cases than other generalized criteria of fixed modes

traveling wave solutions for bistable fractional allen cahn equations with a pyramidal front abstract using the method of sub super solution we construct a solution of s u c u z f u 0 on r 3 of pyramidal shape here s is the fractional laplacian of sub critical order 1 2 s 1 and f is a bistable nonlinearity hence the existence of a traveling wave solution for the parabolic fractional allen cahn equation with pyramidal front is asserted the maximum of planar traveling wave solutions in various directions gives a sub solution a super solution is roughly defined as the one dimensional profile composed with the signed distance to a rescaled mollified pyramid in the main estimate we use an expansion of the fractional laplacian in the fermi coordinates

existence and global stability of traveling curved fronts in the allen cahn equations abstract this paper is concerned with existence and stability of traveling curved fronts for the allen cahn equation in the two dimensional space by using the supersolution and the subsolution we construct a traveling curved front and show that it is the unique traveling wave solution between them our supersolution can be taken arbitrarily large which implies some global asymptotic stability for the traveling curved front

generation and propagation of interfaces for reaction diffusion equations abstract this paper is concerned with the asymptotic behavior as e 0 of the solution ue of the reaction diffusion equation in r n r u t 1 2 0 where is the derivative of a bistable potential we show that if the initial data u 0 has values in both domains of attraction of the potential then an interface will develop in a short time o e 2 ln e we also show that if the wells of the potential are of equal depth then this interface will propagate with normal velocity equal to its mean curvature our result is valid as long as the interface remains smooth if the initial interface is compact and n 2 then the interface will disappear in a finite time but not if n 1 in case the depths of the wells are not equal then in order to obtain get reasonable results we must work on the scaled time s t e slower time scale in this scale we show that the interface moves with a constant speed proportional to the difference of the depths of the two wells along the normal towards the domain of the deeper well this result is valid for all s 0 and does not actually depend on the regularity of the interface we also extend the above results to the homogeneous second initial boundary value problem in case the depths of the wells are equal and the initial interface is orthogonal to the boundary we prove that the interface moves with normal velocity equal to its mean curvature provided that there is a family of hypersurfaces which moves according to their mean curvature and intersect the boundary orthogonally

multidimensional traveling waves in the allen cahn cellular automaton ultradiscretization is a limiting procedure transforming a given difference equation into a cellular automaton the cellular automaton constructed by this procedure preserves the essential properties of the original equation such as the structure of exact solutions for integrable equations in this article a cellular automaton analog of the multidimensional allen cahn equation which is not an integrable system is constructed by the ultradiscretization moreover the traveling wave solutions for the resulting cellular automaton are given the shape behavior and stability of the solutions in ultradiscrete systems are similar to those in continuous systems

technical communique fixed modes in multivariable systems using constrained controllers a general expression is derived relating an arbitrary output feedback controller to the resulting closed loop characteristic polynomial in terms of suitably defined zero polynomials of the system this expression is then used to characterize the fixed modes of a multivariable system with respect to controllers of any desired structure

pyramidal traveling fronts in a nonlocal delayed diffusion equation abstract recently there have been great progresses on the study of nonplanar traveling wave solutions of reaction diffusion equations in this paper we study the pyramidal traveling fronts of nonlocal delayed diffusion equation in r n with n 2 by using the comparison principle and establishing super and subsolution since the effect of nonlocal delay we show that nonlocal delayed diffusion equation in n dimensional space has a pyramidal traveling front u t x v x x n s t toward x n axis for each s c 0 in particular two dimensional traveling curved front and three dimensional pyramidal fronts for nonlocal delayed diffusion equation in r 2 and r 3 are also established respectively moreover we also extend our results to generally nonlocal delayed reaction diffusion equation

equivalence of characterizations of fixed modes abstract in this paper an equivalent property of two matrix rank conditions of a family of matrices is established this equivalent property is then used to show that two well known characterizations of fixed modes are mutually derivable from each other when a minor condition is satisfied

graph theoretic characterization of fixed modes in centralized and decentralized control a closed loop system is represented by a weighted directed graph which exhibits all couplings of the system in a very clear and simple manner the coefficients of the characteristic polynomial of the closed loop system may be obtained with the aid of cycle families in this graph based on this result a criterion for the existence of fixed modes is derived the multiplicities of fixed modes may also be determined graph theoretically the consequences of structural constraints on the output feedback pattern become evident decentralized feedback is discussed as a special case

structurally fixed modes a notion of structurally fixed modes is introduced in the framework of decentralized control systems to identify the modes that cannot be shifted by decentralized feedback regardless of the numerical values of system parameters in this way a qualitative characterization of decentralized fixed modes is provided which is suitable for delineating decentrally stabilizable systems the characterization leads naturally to the notion of fixed modes with respect to arbitrary feedback structure constraints

symmetry of traveling wave solutions to the allen cahn equation in mathbb r 2 in this paper we prove even symmetry of monotone traveling wave solutions to the balanced allen cahn equation in the entire plane related results for the unbalanced allen cahn equation are also discussed

traveling curved fronts of bistable lotka volterra competition diffusion systems in r 3 this paper is concerned with the existence and other qualitative properties of three dimensional traveling curved fronts for bistable lotka volterra competition diffusion systems in r 3 it is first shown that there exists a traveling front of convex polyhedral shape to such systems which is asymptotically stable then by taking the limits of such solutions as lateral surfaces go to infinity one proves the existence as well as the uniqueness of a three dimensional traveling curved front for any given g c s 1 with min 0 2 g 0

asymptotics for nonlinear integral equations with a generalized heat kernel using renormalization group technique in this paper we employ the renormalization group method to study the long time asymptotics of solutions to a class of nonlinear integral equations with a generalized heat kernel the nonlinearities are classified and studied according to its role in the asymptotic behavior here we prove that the behavior in the limit as t goes to infinity remains unchanged when compared with the one in the linear case if the nonlinearities are the ones classified as irrelevant in the renormalization group sense