More on a hyperbolic‐cotangent class of difference equations
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DOI: 10.1002/mma.5541
Abstract: We present a natural method for solving the difference equation read more here.
Keywords: difference; difference equations; cotangent class; class difference ... See more keywords
Admissible meromorphic solutions of algebraic differential‐difference equations
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DOI: 10.1002/mma.5564
Abstract: By using Nevanlinna theory, we generalize a result given by Wittich to complex differential‐difference equations. The result obtained is that the differential‐difference equation in f which is of only one dominant term, has no admissible… read more here.
Keywords: difference; solutions algebraic; meromorphic solutions; difference equations ... See more keywords
Two‐dimensional solvable system of difference equations with periodic coefficients
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DOI: 10.1002/mma.5780
Abstract: We show that the following two‐dimensional system of difference equations: xn+1=anxn+bnyn,yn+1=cnxn+dnyn,n∈N0, where (an)n∈N0 , (bn)n∈N0 , (cn)n∈N0 , and (dn)n∈N0 are periodic sequences, is solvable, considerably extending some results in the literature. In the case… read more here.
Keywords: system; dimensional solvable; difference equations; system difference ... See more keywords
Dynamical properties of some rational systems of difference equations
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DOI: 10.1002/mma.6955
Abstract: We explore the equilibrium points, local and global dynamics, rate of convergence, instability and boundedness of positive solution of some rational systems of difference equations. As an application of difference equations in mathematical biology, we… read more here.
Keywords: difference; properties rational; difference equations; dynamical properties ... See more keywords
Stability and flip bifurcation of a three‐dimensional exponential system of difference equations
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DOI: 10.1002/mma.7031
Abstract: In this paper, we study the stability of the zero equilibrium and the occurrence of flip bifurcation of the following system of difference equations: xn+1=a1ynb1+yn+c1xnek1−d1xn1+ek1−d1xn, yn+1=a2znb2+zn+c2ynek2−d2yn1+ek2−d2yn, zn+1=a3xnb3+xn+c3znek3−d3zn1+ek3−d3zn, where ai, bi, ci, di, and ki, for… read more here.
Keywords: system; difference equations; system difference; stability ... See more keywords
Simultaneous difference equations on a restricted domain
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DOI: 10.1007/s00010-018-0616-x
Abstract: Given a set $$T\subset (0, +\infty )$$T⊂(0,+∞), a function $$c:T\rightarrow \mathbb R$$c:T→R and a real number p we study continuous solutions $$\varphi $$φ of the simultaneous equations $$\begin{aligned} \varphi (tx)=\varphi (x)+c(t)x^p, \qquad t \in T.… read more here.
Keywords: difference equations; simultaneous difference; equations restricted; restricted domain ... See more keywords
Meromorphic Solutions of Certain Nonlinear Difference Equations
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DOI: 10.1007/s00025-021-01414-5
Abstract: Let $$p_1, p_2$$ be nonzero rational functions, $$\alpha _1, \alpha _2$$ be nonzero constants, and $$P_d(z, f)$$ be a difference polynomial in f of degree d. We prove that every finite order meromorphic solution of… read more here.
Keywords: nonlinear difference; difference equations; meromorphic solutions; difference ... See more keywords
Hamiltonian Structures for Integrable Nonabelian Difference Equations
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DOI: 10.1007/s00220-022-04348-3
Abstract: In this paper we extensively study the notion of Hamiltonian structure for nonabelian differential-difference systems, exploring the link between the different algebraic (in terms of double Poisson algebras and vertex algebras) and geometric (in terms… read more here.
Keywords: hamiltonian structures; difference; poisson; integrable nonabelian ... See more keywords
Boundedness, persistence and stability for classes of forced difference equations arising in population ecology
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DOI: 10.1007/s00285-019-01388-7
Abstract: AbstractBoundedness, persistence and stability properties are considered for a class of nonlinear, possibly infinite-dimensional, forced difference equations which arise in a number of ecological and biological contexts. The inclusion of forcing incorporates the effects of… read more here.
Keywords: difference equations; forced difference; persistence stability; stability ... See more keywords
On the Stability of a Linear System of Difference Equations with Random Parameters
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DOI: 10.1007/s10958-018-3784-2
Abstract: We study the asymptotic behavior of solutions to a linear system of difference equation whose right-hand side at each time moment depends not only on the value at the previous moment, but also on a… read more here.
Keywords: system difference; linear system; difference equations; stability linear ... See more keywords
Exponentially Dichotomous Difference Equations with Piecewise Constant Operator Coefficients
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DOI: 10.1007/s11253-020-01835-5
Abstract: We establish necessary and sufficient conditions for the exponential dichotomy of the solutions of linear difference equations with piecewise constant operator coefficients. read more here.
Keywords: difference equations; piecewise constant; operator coefficients; constant operator ... See more keywords